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Optimal Reinsurance And Investment Problem With Default Risk And Bounded Memory
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Book Synopsis Optimal Reinsurance and Investment Problem With Default Risk and Bounded Memory by : Chao Deng
Download or read book Optimal Reinsurance and Investment Problem With Default Risk and Bounded Memory written by Chao Deng and published by . This book was released on 2018 with total page 20 pages. Available in PDF, EPUB and Kindle. Book excerpt: This paper considers an insurer with CARA preference and explores an reinsurance-investment optimization problem where the insurer's income is related to the historical wealth performance. The insurer can purchase proportional reinsurance contracts to transfer the claim risk and allocate the remaining liquid wealth in a saving account, a defaultable corporate zero coupon bond and a risky asset with constant elasticity of variance (CEV) stochastic volatility. The problem is modeled using a stochastic system with delay. Under certain condition, the analytic optimal reinsurance-investment policy is derived and the corresponding verification theorem is provided. Finally, we conduct sensitivity analysis on the optimal reinsurance-investment policies over different memory parameters. The results show that longer memory leads to more prudent reinsurance and investment decisions for the insurer.
Book Synopsis Optimal Per-Loss Reinsurance and Investment Problem Under Negative Correlation Assumption by : Fudong Wang
Download or read book Optimal Per-Loss Reinsurance and Investment Problem Under Negative Correlation Assumption written by Fudong Wang and published by . This book was released on 2023 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this paper, we consider the optimal reinsurance and investment problem for the insurance company, where the insurer can purchase per-loss reinsurance and invest the surplus in a financial market, and the insurer's claim liabilities and capital gains in financial market are negatively correlated which makes our problems more complicated and challenging. We study two optimization problems: minimizing the probability of absolute ruin and maximizing the expected utility of the terminal wealth. By using the dynamic programming and Lagrange multiplier methods, we reduce the infinite-dimensional problem to the one-dimensional problem, and obtain the explicit form of the optimal reinsurance and investment strategies as well as the corresponding value functions. Furthermore, we investigate the impacts of the negative correlation on the optimal strategies, and find that they are totally different in these two problems. For the former, it strongly depends on the wealth level, which means that with the different wealth level, the negative correlation has different influence on the optimal results; but for the latter, both the retained claims and the amount invested in the risky asset increase as the negative correlation becomes stronger.
Book Synopsis Risk Management with Reinsurance Policies by : Han Yu
Download or read book Risk Management with Reinsurance Policies written by Han Yu and published by . This book was released on 2020 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Businesses face various risks that may negatively influence their operations, therefore implementing strategies to deal with risks is important. In recent years, risk management has become an active area of research in finance and insurance. The primary goals of risk management include identifying, assessing and controlling risks to minimize their potential impact. For insurance companies, reinsurance is an effective risk management tool to control risks. As a natural measure of risk, we consider the ruin probability of an insurance business. Our ultimate objective is to evaluate the impact of reinsurance in risk management, particularly in minimizing the ruin probability, and to find the corresponding optimal reinsurance policies. We first study the problem of minimizing the ruin probability in a discrete-time risk model with unknown parameters. A proportional reinsurance is purchased to control the ruin probability. We formulate the problem as a Markov decision process and solve this problem by means of discrete-time dynamic programming. The Bayesian approach is applied to address the issue of parameter uncertainty. We obtain the explicit expressions of minimum ruin probabilities and the corresponding optimal reinsurance strategies. Some structural properties of ruin probabilities are investigated under certain conditions. We also consider an optimization problem by joint decisions of excess-of-loss reinsurance and investment in a continuous-time financial market. The reserve may be invested in a financial market consisting of a risk-free asset and a risky asset with the price process follows geometric Brownian motion. Borrowing is allowed, however, the interest rate of borrowing is higher than the return rate of risk-free. Meanwhile, an excess-of-loss reinsurance is purchased. We apply stochastic control theory and Hamilton-Jacobi-Bellman equation to find the optimal strategy of joint reinsurance and investment decisions, and derive the closed form expression of the minimum ruin probability function. Our results are illustrated numerically. Both theoretical and numerical results show that reinsurance has a significant effect in alleviating the risk of ruin.
Book Synopsis Optimal Reinsurance by : Ka-Chun Joseph Sung
Download or read book Optimal Reinsurance written by Ka-Chun Joseph Sung and published by Open Dissertation Press. This book was released on 2017-01-26 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: This dissertation, "Optimal Reinsurance: a Contemporary Perspective" by Ka-chun, Joseph, Sung, 宋家俊, was obtained from The University of Hong Kong (Pokfulam, Hong Kong) and is being sold pursuant to Creative Commons: Attribution 3.0 Hong Kong License. The content of this dissertation has not been altered in any way. We have altered the formatting in order to facilitate the ease of printing and reading of the dissertation. All rights not granted by the above license are retained by the author. Abstract: In recent years, general risk measures have played an important role in risk management in both finance and insurance industry. As a consequence, there is an increasing number of research on optimal reinsurance problems using risk measures as yard sticks beyond the classical expected utility framework. In this thesis, the stop-loss reinsurance is first shown to be an optimal contract under law-invariant convex risk measures via a new simple geometric argument. This similar approach is then used to tackle the same optimal reinsurance problem under Value at Risk and Conditional Tail Expectation; it is interesting to note that, instead of stop-loss reinsurances, insurance layers serve as the optimal solution in these cases. These two results hint that law-invariant convex risk measure may be better and more robust to expected larger claims than Value at Risk and Conditional Tail Expectation even though they are more commonly used. In addition, the problem of optimal reinsurance design for a basket of n insurable risks is studied. Without assuming any particular dependence structure, a minimax optimal reinsurance decision formulation for the problem has been successfully proposed. To solve it, the least favorable dependence structure is first identified, and then the stop-loss reinsurances are shown to minimize a general law-invariant convex risk measure of the total retained risk. Sufficient condition for ordering the optimal deductibles are also obtained. Next, a Principal-Agent model is adopted to describe a monopolistic reinsurance market with adverse selection. Under the asymmetry of information, the reinsurer (the principal) aims to maximize the average profit by selling a tailor-made reinsurance to every insurer (agent) from a (huge) family with hidden characteristics. In regard to Basel Capital Accord, each insurer uses Value at Risk as the risk assessment, and also takes the right to choose different risk tolerances. By utilizing the special features of insurance layers, their optimality as the first-best strategy over all feasible reinsurances is proved. Also, the same optimal reinsurance screening problem is studied under other subclass of reinsurances: (i) deductible contracts; (ii) quota-share reinsurances; and (iii) reinsurance contracts with convex indemnity, with the aid of indirect utility functions. In particular, the optimal indirect utility function is shown to be of the stop-loss form under both classes (i) and (ii); while on the other hand, its non-stop-loss nature under class (iii) is revealed. Lastly, a class of nonzero-sum stochastic differential reinsurance games between two insurance companies is studied. Each insurance company is assumed to maximize the difference of the opponent's terminal surplus from that of its own by properly arranging its reinsurance schedule. The surplus process of each insurance company is modeled by a mixed regime-switching Cramer-Lundberg approximation. It is a diffusion risk process with coefficients being modulated by both a continuous-time finite-state Markov Chain and another diffusion process; and correlations among these surplus processes are allowed. In contrast to the tradit
Book Synopsis Risk Measures and Optimal Reinsurance by : Fangda Liu
Download or read book Risk Measures and Optimal Reinsurance written by Fangda Liu and published by . This book was released on 2015 with total page 133 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this thesis, we study the optimal reinsurance design problem and extend the classical model in three different directions: (1) In the first framework, we add the additional assumption that the reinsurer can default on its obligations. If the indemnity is beyond the reinsurer's payment ability, the reinsurer fails to pay for the exceeding part and this induces a default risk for the insurer. In our model, the reinsurer is assumed to measure the risk of an insured loss by Value-at-Risk regulation and prepares the same amount of money as the initial reserve. As soon as the indemnity is larger than this value plus the premium, default occurs. From the insurer's point of view, two optimization problems are going to be considered when the insurer: 1) maximizes his expectation of utility; 2) minimizes the VaR of his retained loss. (2) In the second framework, the reinsurance buyer (insurer) adopts a convex risk measure to control his total loss while the reinsurance seller (reinsurer) price the reinsurance contract by Wang's premium principle with a distortion. Without specifying a particular convex risk measure and distortion, we obtain a general expression for the optimal reinsurance contract that minimizes the insurer's total risk exposure. (3) In the third framework, we study optimal reinsurance designs from the perspectives of both an insurer and a reinsurer and take into account both an insurer's aims and a reinsurer's goals in reinsurance contract designs. We develop optimal reinsurance contracts that minimize the convex combination of the VaR risk measures of the insurer's loss and the reinsurer's loss under two types of constraints, respectively. The constraints describe the interest of both the insurer and the reinsurer. With the first type of constraints, the insurer and the reinsurer each have their limit on the VaR of their own loss. With the second type of constraints, the insurer has a limit on the VaR of his loss while the reinsurer has a target on his profit from selling a reinsurance contract. For both types of constraints, we derive the optimal reinsurance form for a wide class of reinsurance policies and under the expected value reinsurance premium principle.
Book Synopsis Non-Zero-Sum Stochastic Differential Reinsurance and Investment Games with Default Risk by : Chao Deng
Download or read book Non-Zero-Sum Stochastic Differential Reinsurance and Investment Games with Default Risk written by Chao Deng and published by . This book was released on 2018 with total page 32 pages. Available in PDF, EPUB and Kindle. Book excerpt: This paper investigates implications of strategic interaction (competition) between two CARA insurers on their reinsurance and investment policies. The two insurers are concerned about their terminal wealth as well as the relative performance measured by the difference between their terminal wealth. The problem of finding optimal policies for the both insurers is modeled by a non-zero-sum stochastic differential game. We assume that the insurers can invest in a risky asset with Heston's stochastic volatility and a defautable corporate bond, and the reinsurance premium is calculated by the variance premium principle. We derive the Nash equilibrium reinsurance policy and investment policy explicitly for the game and prove the corresponding verification theorem. The equilibrium strategy indicates that the best response of each insurer to the competition is to mimic the strategy of its opponent. As a consequence, the reinsurance and investment strategy of an insurer with the relative performance concern is riskier than that without the concern. We illustrate our results by numerical examples.
Book Synopsis Optimal Reinsurance in the Presence of Counterparty Default Risk by : Alexandru Vali Asimit
Download or read book Optimal Reinsurance in the Presence of Counterparty Default Risk written by Alexandru Vali Asimit and published by . This book was released on 2014 with total page 17 pages. Available in PDF, EPUB and Kindle. Book excerpt: The optimal reinsurance arrangement is identified whenever the reinsurer counterparty default risk is incorporated in a one-period model. Our default risk model allows the possibility for the reinsurer to fail paying in full the promised indemnity, whenever it exceeds the level of regulatory capital. We also investigate the change in the optimal solution if the reinsurance premium recognises or not the default in payment. Closed form solutions are elaborated when the insurer's objective function is set via some well-known risk measures. It is also discussed the effect of reinsurance over the policyholder welfare. If the insurer is Value-at-Risk regulated, then the reinsurance does not increase the policyholder's exposure for any possible reinsurance transfer, even if the reinsurer may default in paying the promised indemnity. Numerical examples are also provided in order to illustrate and conclude our findings. It is found that the optimal reinsurance contract does not usually change if the counterparty default risk is taken into account, but one should consider this effect in order to properly measure the policyholders's exposure. In addition, the counterparty default risk may change the insurer's ideal arrangement if the buyer and seller have very different views on the reinsurer's recovery rate.
Book Synopsis Optimal Risk Control with Investment Decisions by : Yu Zhang
Download or read book Optimal Risk Control with Investment Decisions written by Yu Zhang and published by . This book was released on 2020 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Modern businesses face different kinds of risk that may affect their management operations and cause significant financial losses. It is thus very crucial to identify, assess and control risks to reduce their potential impact. One important objective for insurance businesses is implementing strategies to control the risk of ruin, which is naturally measured by the ruin probability. In this study, we consider optimal risk control problems with investment decisions and aim to assess the impact of investment on minimizing the ruin probability. Specifically, we apply stochastic control in insurance to determine optimal investment strategies. We first consider the problem of controlling ruin probability by investment decisions under a discrete-time risk process. An insurance company may invest its reserve into a riskless asset and a risky asset. Our goal is concentrated on finding the optimal investment strategy to minimize the ruin probability, in the case that the claim size distribution has an unknown mean parameter. Applying the Bayesian approach and the dynamic programming method, we find the minimal ruin probability function and the corresponding optimal investment decisions. We also investigate some structural properties of the optimal strategy. We investigate the problem of minimizing the ruin probability with joint decisions of investment and excess-of-loss reinsurance for a continuous-time risk model. The reserve of an insurance company is modeled by a diffusion process and may be invested in a financial market which follows the Black-Scholes model consisting of a risky asset and a riskless asset. However, a constraint is imposed on investment decisions and the ratio between the amount invested in the risky asset and the total reserve should lie below a given bound. Meanwhile, the insurance company may purchase an excess-of-loss reinsurance to reduce risk. We characterize and derive jointly optimal decisions of investment and reinsurance to minimize ruin probability. We solve the corresponding Hamilton-Jacobi-Bellman equation and provide an explicit form for the minimal ruin probability function. In addition, we present several numerical examples to illustrate our results, which indicate a positive impact of investment on controlling the risk of ruin.
Book Synopsis Optimal Reinsurance Designs by : Chengguo Weng
Download or read book Optimal Reinsurance Designs written by Chengguo Weng and published by . This book was released on 2009 with total page 212 pages. Available in PDF, EPUB and Kindle. Book excerpt: The research on optimal reinsurance design dated back to the 1960's. For nearly half a century, the quest for optimal reinsurance designs has remained a fascinating subject, drawing significant interests from both academicians and practitioners. Its fascination lies in its potential as an effective risk management tool for the insurers. There are many ways of formulating the optimal design of reinsurance, depending on the chosen objective and constraints. In this thesis, we address the problem of optimal reinsurance designs from an insurer's perspective. For an insurer, an appropriate use of the reinsurance helps to reduce the adverse risk exposure and improve the overall viability of the underlying business. On the other hand, reinsurance incurs additional cost to the insurer in the form of reinsurance premium. This implies a classical risk and reward tradeoff faced by the insurer. The primary objective of the thesis is to develop theoretically sound and yet practical solution in the quest for optimal reinsurance designs. In order to achieve such an objective, this thesis is divided into two parts. In the first part, a number of reinsurance models are developed and their optimal reinsurance treaties are derived explicitly. This part focuses on the risk measure minimization reinsurance models and discusses the optimal reinsurance treaties by exploiting two of the most common risk measures known as the Value-at-Risk (VaR) and the Conditional Tail Expectation (CTE). Some additional important economic factors such as the reinsurance premium budget, the insurer's profitability are also considered. The second part proposes an innovative method in formulating the reinsurance models, which we refer as the empirical approach since it exploits explicitly the insurer's empirical loss data. The empirical approach has the advantage that it is practical and intuitively appealing. This approach is motivated by the difficulty that the reinsurance models are often infinite dimensional optimization problems and hence the explicit solutions are achievable only in some special cases. The empirical approach effectively reformulates the optimal reinsurance problem into a finite dimensional optimization problem. Furthermore, we demonstrate that the second-order conic programming can be used to obtain the optimal solutions for a wide range of reinsurance models formulated by the empirical approach.
Book Synopsis Time-Consistent Investment-Reinsurance Strategy for Mean-Variance Insurers With a Defaultable Security by : Hui Zhao
Download or read book Time-Consistent Investment-Reinsurance Strategy for Mean-Variance Insurers With a Defaultable Security written by Hui Zhao and published by . This book was released on 2015 with total page 27 pages. Available in PDF, EPUB and Kindle. Book excerpt: This paper considers an optimal investment and reinsurance problem involving a defaultable security for an insurer under the mean-variance criterion in a jump-diffusion risk model. The insurer is allowed to purchase proportional reinsurance or acquire new business and invest in a financial market consisting of a risk-free bank account, a stock and a defaultable bond. From a game theoretic perspective, the extended Hamilton-Jacobi-Bellman systems are established for the post-default case and the pre-default case, respectively. Furthermore, for the two cases, closed-form expressions for the optimal time-consistent investment-reinsurance strategies and the corresponding optimal value functions are derived, and some properties of the strategies are analyzed. Finally, some special cases of our model are presented, and numerical analysis is provided to illustrate our results.
Book Synopsis Modern Actuarial Risk Theory by : Rob Kaas
Download or read book Modern Actuarial Risk Theory written by Rob Kaas and published by Springer Science & Business Media. This book was released on 2008-12-03 with total page 394 pages. Available in PDF, EPUB and Kindle. Book excerpt: Modern Actuarial Risk Theory contains what every actuary needs to know about non-life insurance mathematics. It starts with the standard material like utility theory, individual and collective model and basic ruin theory. Other topics are risk measures and premium principles, bonus-malus systems, ordering of risks and credibility theory. It also contains some chapters about Generalized Linear Models, applied to rating and IBNR problems. As to the level of the mathematics, the book would fit in a bachelors or masters program in quantitative economics or mathematical statistics. This second and.
Download or read book Munich Re written by Johannes Bähr and published by C.H.Beck. This book was released on 2016-10-27 with total page 379 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Reinsurance has to be international in accordance with its nature." This is the well-known viewpoint of Carl von Thieme, one of the founders of Munich Re, who also served as its general director for many years. Thus, it was not a coincidence that the company rose to become the world market leader rather quickly after its founding in 1880. In the following period, Munich Re stayed on top or was occasionally second to Swiss Re. Nonetheless, the broader public does not know much about the company. Johannes Bähr and Christopher Kopper now present the first history of the reinsurer from its beginnings into the 1980s. Few companies have risen to become world market leaders as quickly as Munich Re, and only the fewest have succeeded in remaining at the top of the world market for as long. The company’s history reveals how insurers reacted to major catastrophes and technological shifts. Without sharing risks with reinsurers, countless direct insurers would not have survived the economic consequences of major natural catastrophes and would have been forced into bankruptcy by the weight of their payment obligations. Consequently, reinsurers even made coverage for some risks possible in the first place. Yet Munich Re itself also repeatedly contributed to the introduction of new segments of insurance, such as in the case of machine insurance or high-risk life insurance. Thus, the history of this pioneer of globalization is, at the same time, a history of dealing with risks and managing the distribution of risk. Last but not least, it is also the history of a German company that profited from the National Socialist dictatorship and, with great effort, had to find its way back into the world market after the two world wars.
Book Synopsis Investment Guarantees by : Mary Hardy
Download or read book Investment Guarantees written by Mary Hardy and published by John Wiley & Sons. This book was released on 2003-03-06 with total page 309 pages. Available in PDF, EPUB and Kindle. Book excerpt: A comprehensive guide to investment guarantees in equity-linked life insurance Due to the convergence of financial and insurance markets, new forms of investment guarantees are emerging which require financial service professionals to become savvier in modeling and risk management. With chapters that discuss stock return models, dynamic hedging, risk measures, Markov Chain Monte Carlo estimation, and much more, this one-stop reference contains the valuable insights and proven techniques that will allow readers to better understand the theory and practice of investment guarantees and equity-linked insurance policies. Mary Hardy, PhD (Waterloo, Ontario, Canada), is an Associate Professor and Associate Chair of Actuarial Science at the University of Waterloo and is a Fellow of the Institute of Actuaries and an Associate of the Society of Actuaries, where she is a frequent speaker. Her research covers topics in life insurance solvency and risk management, with particular emphasis on equity-linked insurance. Hardy is an Associate Editor of the North American Actuarial Journal and the ASTIN Bulletin and is a Deputy Editor of the British Actuarial Journal.
Book Synopsis Applications of Stochastic Optimal Control to Economics and Finance by : Salvatore Federico
Download or read book Applications of Stochastic Optimal Control to Economics and Finance written by Salvatore Federico and published by . This book was released on 2020-06-23 with total page 206 pages. Available in PDF, EPUB and Kindle. Book excerpt: In a world dominated by uncertainty, modeling and understanding the optimal behavior of agents is of the utmost importance. Many problems in economics, finance, and actuarial science naturally require decision makers to undertake choices in stochastic environments. Examples include optimal individual consumption and retirement choices, optimal management of portfolios and risk, hedging, optimal timing issues in pricing American options, and investment decisions. Stochastic control theory provides the methods and results to tackle all such problems. This book is a collection of the papers published in the Special Issue "Applications of Stochastic Optimal Control to Economics and Finance", which appeared in the open access journal Risks in 2019. It contains seven peer-reviewed papers dealing with stochastic control models motivated by important questions in economics and finance. Each model is rigorously mathematically funded and treated, and the numerical methods are employed to derive the optimal solution. The topics of the book's chapters range from optimal public debt management to optimal reinsurance, real options in energy markets, and optimal portfolio choice in partial and complete information settings. From a mathematical point of view, techniques and arguments of dynamic programming theory, filtering theory, optimal stopping, one-dimensional diffusions and multi-dimensional jump processes are used.
Book Synopsis How I Became a Quant by : Richard R. Lindsey
Download or read book How I Became a Quant written by Richard R. Lindsey and published by John Wiley & Sons. This book was released on 2011-01-11 with total page 406 pages. Available in PDF, EPUB and Kindle. Book excerpt: Praise for How I Became a Quant "Led by two top-notch quants, Richard R. Lindsey and Barry Schachter, How I Became a Quant details the quirky world of quantitative analysis through stories told by some of today's most successful quants. For anyone who might have thought otherwise, there are engaging personalities behind all that number crunching!" --Ira Kawaller, Kawaller & Co. and the Kawaller Fund "A fun and fascinating read. This book tells the story of how academics, physicists, mathematicians, and other scientists became professional investors managing billions." --David A. Krell, President and CEO, International Securities Exchange "How I Became a Quant should be must reading for all students with a quantitative aptitude. It provides fascinating examples of the dynamic career opportunities potentially open to anyone with the skills and passion for quantitative analysis." --Roy D. Henriksson, Chief Investment Officer, Advanced Portfolio Management "Quants"--those who design and implement mathematical models for the pricing of derivatives, assessment of risk, or prediction of market movements--are the backbone of today's investment industry. As the greater volatility of current financial markets has driven investors to seek shelter from increasing uncertainty, the quant revolution has given people the opportunity to avoid unwanted financial risk by literally trading it away, or more specifically, paying someone else to take on the unwanted risk. How I Became a Quant reveals the faces behind the quant revolution, offering you?the?chance to learn firsthand what it's like to be a?quant today. In this fascinating collection of Wall Street war stories, more than two dozen quants detail their roots, roles, and contributions, explaining what they do and how they do it, as well as outlining the sometimes unexpected paths they have followed from the halls of academia to the front lines of an investment revolution.
Book Synopsis Optimal Control and Partial Differential Equations by : José Luis Menaldi
Download or read book Optimal Control and Partial Differential Equations written by José Luis Menaldi and published by IOS Press. This book was released on 2001 with total page 632 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains more than sixty invited papers of international wellknown scientists in the fields where Alain Bensoussan's contributions have been particularly important: filtering and control of stochastic systems, variationnal problems, applications to economy and finance, numerical analysis... In particular, the extended texts of the lectures of Professors Jens Frehse, Hitashi Ishii, Jacques-Louis Lions, Sanjoy Mitter, Umberto Mosco, Bernt Oksendal, George Papanicolaou, A. Shiryaev, given in the Conference held in Paris on December 4th, 2000 in honor of Professor Alain Bensoussan are included.
Book Synopsis The Microeconomics of Insurance by : Ray Rees
Download or read book The Microeconomics of Insurance written by Ray Rees and published by Now Publishers Inc. This book was released on 2008 with total page 178 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this relatively short survey, we present the core elements of the microeconomic analysis of insurance markets at a level suitable for senior undergraduate and graduate economics students. The aim of this analysis is to understand how insurance markets work, what their fundamental economic functions are, and how efficiently they may be expected to carry these out.
