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Non Zero Sum Stochastic Differential Reinsurance Game And Optimal Asset Allocation With Restriction On Liquidity
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Book Synopsis Non-Zero-Sum Stochastic Differential Reinsurance Game and Optimal Asset Allocation with Restriction on Liquidity by : Chuan Xu
Download or read book Non-Zero-Sum Stochastic Differential Reinsurance Game and Optimal Asset Allocation with Restriction on Liquidity written by Chuan Xu and published by . This book was released on 2020 with total page 96 pages. Available in PDF, EPUB and Kindle. Book excerpt:
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 Determining the Insurer's Optimal Investment and Reinsurance Strategy Based on Stochastic Differential Game by : Hong Mao
Download or read book Determining the Insurer's Optimal Investment and Reinsurance Strategy Based on Stochastic Differential Game written by Hong Mao and published by . This book was released on 2015 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this paper, we discuss how to determine the optimal investment portfolio and reinsurance strategy of insurance company based on zero-sum stochastic differential game between the market and the insurer. We extend Zhang and Siu (2009)'s model by (1) including a risk-free asset, (2) considering risky assets instead of only one risky asset and (3) discussing the case of power utility function besides exponential utility when the wealth process of an insurance company is a diffusion process. We establish the Hamilton-Jacobi-Bellman-Issacs equations and obtain the optimal solutions of the amount invested in risky assets and retention of reinsurance. Our results show that the optimal solution is positively correlated to time but independent of the wealth of insurer, when the utility function of terminal wealth is exponential. However, the optimal solution is uncorrelated to time and is increasing function of the wealth of the insurer in the case of power utility function. Our results also show that the risk-free interest rate will affect the strategy of investment and reinsurance.
Book Synopsis Non-zero-sum Stochastic Differential Games for Asset-liability Management with Stochastic Inflation and Stochastic Volatility by : Yumo Zhang
Download or read book Non-zero-sum Stochastic Differential Games for Asset-liability Management with Stochastic Inflation and Stochastic Volatility written by Yumo Zhang and published by . This book was released on 2022 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This paper investigates the optimal asset-liability management problems for two managers subject to relative performance concerns in the presence of stochastic inflation and stochastic volatility. The objective of the two managers is to maximize the expected utility of their relative terminal surplus with respect to that of their competitor. The problem of finding the optimal investment strategies for both managers is modelled as a non-zero-sum stochastic differential game. Both managers have access to a financial market consisting of a risk-free asset, a risky asset, and an inflation-linked index bond. The risky asset's price process and uncontrollable random liabilities are not only affected by the inflation risk but also driven by a general class of stochastic volatility models including the constant elasticity of variance model, the family of state-of-the-art 4/2 models, and some path-dependent models as particular cases. By adopting a backward stochastic differential equation (BSDE) approach to overcome the possibly non-Markovian setting, closed-form expressions for the equilibrium investment strategies and corresponding value functions are derived under power and exponential utility preferences. Moreover, explicit solutions to some special cases of our model are provided. Finally, we perform numerical studies to illustrate the impact of model parameters on the equilibrium strategies and draw some economic interpretations.
Book Synopsis Robust Non-Zero-Sum Stochastic Differential Investment-Reinsurance Game by : Chi Seng Pun
Download or read book Robust Non-Zero-Sum Stochastic Differential Investment-Reinsurance Game written by Chi Seng Pun and published by . This book was released on 2017 with total page 26 pages. Available in PDF, EPUB and Kindle. Book excerpt: This paper considers the non-zero-sum stochastic differential game problem between two ambiguity-averse insurers (AAIs) who encounter model uncertainty and seek the optimal investment and reinsurance decision under relative performance concerns. Each AAI invests in a risky asset and a risk-free asset, and manages her own risks by purchasing reinsurance with the objective of maximizing the expected utility of her relative terminal surplus with respect to that of her counterparty. The two AAIs' decisions influence each other through the insurers' relative performance concerns and the correlation between their surplus processes. We establish a general framework of Nash equilibrium for the associated non-zero-sum game with model uncertainty. For the representative case of exponential utilities and the Heston model, we solve the equilibrium strategies explicitly. Numerical studies are conducted to draw economic interpretations.
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 Non-zero-sum Reinsurance Games Subject to Ambiguous Correlations by : Chi Seng Pun
Download or read book Non-zero-sum Reinsurance Games Subject to Ambiguous Correlations written by Chi Seng Pun and published by . This book was released on 2020 with total page 20 pages. Available in PDF, EPUB and Kindle. Book excerpt: This paper studies the economic implications of ambiguous correlation in a non-zero-sum game between two insurers. We establish the general framework of Nash equilibrium for the coupled optimization problems. For the constant absolute risk aversion (CARA) insurers, we show that the equilibrium reinsurance strategies admit closed-form solutions. Our results indicate that the ambiguous correlation leads to an increase in the equilibrium demand of reinsurance protection for both insurers. Numerical studies examine the effect on the quality of the correlation estimations.
Book Synopsis Time Inconsistent Stochastic Differential Game by : Hong Mao
Download or read book Time Inconsistent Stochastic Differential Game written by Hong Mao and published by . This book was released on 2018 with total page 35 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this paper, time-inconsistent model was established under stochastic differential game framework. The investment portfolio includes multi-risky assets, whose returns are assumed to be correlated in a time-varying manner and change cyclically. The claim losses of insurance companies and investment are also assumed to be correlated with each other. The Solution to extended HJBI equations results in the portion of retention and an optimal portfolio with equally weighted allocations of risky assets. An optimal control bound is proposed for monitoring and predicting the optimal wealth level. The proposed model is expected to be effective in making decision for investment and reinsurance strategies, controlling and predicting optimal wealth under uncertain environment. Especially, it can be applied easily in the situation of very high dimensional investment portfolio.
Book Synopsis Risk Analysis and Portfolio Modelling by : Elisa Luciano
Download or read book Risk Analysis and Portfolio Modelling written by Elisa Luciano and published by MDPI. This book was released on 2019-10-16 with total page 224 pages. Available in PDF, EPUB and Kindle. Book excerpt: Financial Risk Measurement is a challenging task, because both the types of risk and the techniques evolve very quickly. This book collects a number of novel contributions to the measurement of financial risk, which address either non-fully explored risks or risk takers, and does so in a wide variety of empirical contexts.
Book Synopsis Backward Stochastic Differential Equations by : N El Karoui
Download or read book Backward Stochastic Differential Equations written by N El Karoui and published by CRC Press. This book was released on 1997-01-17 with total page 236 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents the texts of seminars presented during the years 1995 and 1996 at the Université Paris VI and is the first attempt to present a survey on this subject. Starting from the classical conditions for existence and unicity of a solution in the most simple case-which requires more than basic stochartic calculus-several refinements on the hypotheses are introduced to obtain more general results.
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 Macroprudential Solvency Stress Testing of the Insurance Sector by : Mr.Andreas A. Jobst
Download or read book Macroprudential Solvency Stress Testing of the Insurance Sector written by Mr.Andreas A. Jobst and published by International Monetary Fund. This book was released on 2014-07-22 with total page 84 pages. Available in PDF, EPUB and Kindle. Book excerpt: Over the last decade, stress testing has become a central aspect of the Fund’s bilateral and multilateral surveillance work. Recently, more emphasis has also been placed on the role of insurance for financial stability analysis. This paper reviews the current state of system-wide solvency stress tests for insurance based on a comparative review of national practices and the experiences from Fund’s FSAP program with the aim of providing practical guidelines for the coherent and consistent implementation of such exercises. The paper also offers recommendations on improving the current insurance stress testing approaches and presentation of results.
Book Synopsis Handbook of Hedge Funds by : François-Serge Lhabitant
Download or read book Handbook of Hedge Funds written by François-Serge Lhabitant and published by John Wiley & Sons. This book was released on 2011-03-23 with total page 654 pages. Available in PDF, EPUB and Kindle. Book excerpt: A comprehensive guide to the burgeoning hedge fund industry Intended as a comprehensive reference for investors and fund and portfolio managers, Handbook of Hedge Funds combines new material with updated information from Francois-Serge L’habitant’s two other successful hedge fund books. This book features up-to-date regulatory and historical information, new case studies and trade examples, detailed analyses of investment strategies, discussions of hedge fund indices and databases, and tips on portfolio construction. Francois-Serge L’habitant (Geneva, Switzerland) is the Head of Investment Research at Kedge Capital. He is Professor of Finance at the University of Lausanne and at EDHEC Business School, as well as the author of five books, including Hedge Funds: Quantitative Insights (0-470-85667-X) and Hedge Funds: Myths & Limits (0-470-84477-9), both from Wiley.
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 Economic and Financial Decisions under Risk by : Louis Eeckhoudt
Download or read book Economic and Financial Decisions under Risk written by Louis Eeckhoudt and published by Princeton University Press. This book was released on 2011-10-30 with total page 245 pages. Available in PDF, EPUB and Kindle. Book excerpt: An understanding of risk and how to deal with it is an essential part of modern economics. Whether liability litigation for pharmaceutical firms or an individual's having insufficient wealth to retire, risk is something that can be recognized, quantified, analyzed, treated--and incorporated into our decision-making processes. This book represents a concise summary of basic multiperiod decision-making under risk. Its detailed coverage of a broad range of topics is ideally suited for use in advanced undergraduate and introductory graduate courses either as a self-contained text, or the introductory chapters combined with a selection of later chapters can represent core reading in courses on macroeconomics, insurance, portfolio choice, or asset pricing. The authors start with the fundamentals of risk measurement and risk aversion. They then apply these concepts to insurance decisions and portfolio choice in a one-period model. After examining these decisions in their one-period setting, they devote most of the book to a multiperiod context, which adds the long-term perspective most risk management analyses require. Each chapter concludes with a discussion of the relevant literature and a set of problems. The book presents a thoroughly accessible introduction to risk, bridging the gap between the traditionally separate economics and finance literatures.
Download or read book Credit Risk written by Darrell Duffie and published by Princeton University Press. This book was released on 2012-01-12 with total page 415 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this book, two of America's leading economists provide the first integrated treatment of the conceptual, practical, and empirical foundations for credit risk pricing and risk measurement. Masterfully applying theory to practice, Darrell Duffie and Kenneth Singleton model credit risk for the purpose of measuring portfolio risk and pricing defaultable bonds, credit derivatives, and other securities exposed to credit risk. The methodological rigor, scope, and sophistication of their state-of-the-art account is unparalleled, and its singularly in-depth treatment of pricing and credit derivatives further illuminates a problem that has drawn much attention in an era when financial institutions the world over are revising their credit management strategies. Duffie and Singleton offer critical assessments of alternative approaches to credit-risk modeling, while highlighting the strengths and weaknesses of current practice. Their approach blends in-depth discussions of the conceptual foundations of modeling with extensive analyses of the empirical properties of such credit-related time series as default probabilities, recoveries, ratings transitions, and yield spreads. Both the "structura" and "reduced-form" approaches to pricing defaultable securities are presented, and their comparative fits to historical data are assessed. The authors also provide a comprehensive treatment of the pricing of credit derivatives, including credit swaps, collateralized debt obligations, credit guarantees, lines of credit, and spread options. Not least, they describe certain enhancements to current pricing and management practices that, they argue, will better position financial institutions for future changes in the financial markets. Credit Risk is an indispensable resource for risk managers, traders or regulators dealing with financial products with a significant credit risk component, as well as for academic researchers and students.
Book Synopsis Statistical Pattern Recognition by : Andrew R. Webb
Download or read book Statistical Pattern Recognition written by Andrew R. Webb and published by John Wiley & Sons. This book was released on 2003-07-25 with total page 516 pages. Available in PDF, EPUB and Kindle. Book excerpt: Statistical pattern recognition is a very active area of study andresearch, which has seen many advances in recent years. New andemerging applications - such as data mining, web searching,multimedia data retrieval, face recognition, and cursivehandwriting recognition - require robust and efficient patternrecognition techniques. Statistical decision making and estimationare regarded as fundamental to the study of pattern recognition. Statistical Pattern Recognition, Second Edition has been fullyupdated with new methods, applications and references. It providesa comprehensive introduction to this vibrant area - with materialdrawn from engineering, statistics, computer science and the socialsciences - and covers many application areas, such as databasedesign, artificial neural networks, and decision supportsystems. * Provides a self-contained introduction to statistical patternrecognition. * Each technique described is illustrated by real examples. * Covers Bayesian methods, neural networks, support vectormachines, and unsupervised classification. * Each section concludes with a description of the applicationsthat have been addressed and with further developments of thetheory. * Includes background material on dissimilarity, parameterestimation, data, linear algebra and probability. * Features a variety of exercises, from 'open-book' questions tomore lengthy projects. The book is aimed primarily at senior undergraduate and graduatestudents studying statistical pattern recognition, patternprocessing, neural networks, and data mining, in both statisticsand engineering departments. It is also an excellent source ofreference for technical professionals working in advancedinformation development environments. For further information on the techniques and applicationsdiscussed in this book please visit ahref="http://www.statistical-pattern-recognition.net/"www.statistical-pattern-recognition.net/a
