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Optimal Investment Strategy To Maximize The Expected Utility Of An Insurance Company Under Cramer Lundberg Dynamic
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Book Synopsis Optimal Investment Strategy to Maximize the Expected Utility of an Insurance Company Under Cramer-Lundberg Dynamic by : Jose Cerda Hernández
Download or read book Optimal Investment Strategy to Maximize the Expected Utility of an Insurance Company Under Cramer-Lundberg Dynamic written by Jose Cerda Hernández and published by . This book was released on 2022 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this work, we examine the combined problem of optimal portfolio selection rules for an insurer in a continuous-time model where the surplus of an insurance company is modelled as a compound Poisson process. The company can invest its surplus in a risk free asset and in a risky asset, governed by the Black-Scholes equation.According to utility theory, in a financial market where investors are facing uncertainty, an investor is not concerned with wealth maximization per se but with utility maximization. It is therefore possible to introduce an increasing and concave utility function $ phi(x,t)$ representing the expected utility of a risk averse investor (insurance company). Therefore, the goal of this work is not anymore to maximize the expected portfolio value or minimize the ruin probability or maximizing the expectation of the present value of all dividends paid to the shareholders up to the ruin, but to maximize the expected utility stemming from the wealth during the life contract $[0,T]$. In this direction, using the Dynamic Programming Principle of the problem, we obtain the Hamilton-Jacobi- Bellman equation by our optimization problem (HJB). Finally, we present numerical solutions in some cases, obtaining as optimal strategy the well known Merton's strategy.
Book Synopsis Optimal Decision on Dynamic Insurance Price and Investment Portfolio of an Insurer in a Competitive Market by : Krzysztof Ostaszewski
Download or read book Optimal Decision on Dynamic Insurance Price and Investment Portfolio of an Insurer in a Competitive Market written by Krzysztof Ostaszewski and published by . This book was released on 2011 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this article, we establish a model of insurance pricing with the assumptions that the insurance price, investment returns and insured losses are correlated stochastic processes, while also considering the affect of the demand on the price. The objective of the pricing model is to maximize the expected utility of the terminal wealth of an insurer. We construct a Hamilton-Jacobi-Bellman (HJB) equation and determine the optimal price of an insurance product and optimal investment portfolio of an insurer simultaneously by solving that HJB equation. We also carry out sensitivity analysis. The results of our analysis show that elasticity of insurance demand greatly affects the optimal solutions. Notably, quantity of insurance demanded affects the optimal allocation to risky assets in the insurer's investment portfolio. Therefore, the demand function for insurance must be considered in management of insurance firm. Our results also show that the drift and volatility of the process of insurance price will affect the investment strategy, in addition to the effect of the drift and volatility of investment process itself. Finally, the drift and volatility of investment stochastic process will affect the insurance price in the cases when the elasticity of demand is large, but that influence is negligible with small elasticity of demand.
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 Optimal Decision on Dynamic Insurance Price and Investment Portfolio of An Insurer with Multi-Dimensional Time-Varying Correlation by : Hong Mao
Download or read book Optimal Decision on Dynamic Insurance Price and Investment Portfolio of An Insurer with Multi-Dimensional Time-Varying Correlation 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 article, a model of optimal insurance pricing and investment strategies is established. The insurance price, investment returns and insured losses are assumed to be correlated stochastic processes. N kinds of invested risky assets following multi-Vasicek model with time-varying correlation are discussed in the investment portfolio. Demand of insurance contracts is considered to affect the price of the contracts. The utility is a performance process and is specified for time t and t is equal to or greater than zero. Dynamical optimal price of an insurance contract and the optimal investment portfolio of an insurer are found simultaneously by maximizing the performance of the insurer. Finally, numerical analysis is carried out with an example. The results show that Treasure Bills, generally considered as a risk-free asset, has been examined to follow the similar pattern as other risky assets in the long run; multi-Vasicek model is an appropriate model to describe the change pattern of the return of risky assets invested. The sensitivity of the change of important parameters on the optimal solutions is analyzed. Particularly, the equally weighted investment portfolio can be an optimal investment strategy under some conditions. The proposed model in this paper can be used to obtain optimal solutions easily even in the situation of high dimensional investment portfolio.
Book Synopsis Innovations In Insurance, Risk- And Asset Management - Proceedings Of The Innovations In Insurance, Risk- And Asset Management Conference by : Kathrin Glau
Download or read book Innovations In Insurance, Risk- And Asset Management - Proceedings Of The Innovations In Insurance, Risk- And Asset Management Conference written by Kathrin Glau and published by World Scientific. This book was released on 2018-09-14 with total page 468 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book covers recent developments in the interdisciplinary fields of actuarial science, quantitative finance, risk- and asset management. The authors are leading experts from academia and practice who participated in Innovations in Insurance, Risk- and Asset Management, an international conference held at the Technical University of Munich in 2017.The topics covered include the mathematics of extreme risks, systemic risk, model uncertainty, interest rate and hybrid models, alternative investments, dynamic investment strategies, quantitative risk management, asset liability management, liability driven investments, and behavioral finance.This timely selection of topics is highly relevant for the financial industry and addresses current issues both from an academic as well as from a practitioner's point of view.
Book Synopsis Optimal Portfolios with Stochastic Interest Rates and Defaultable Assets by : Holger Kraft
Download or read book Optimal Portfolios with Stochastic Interest Rates and Defaultable Assets written by Holger Kraft and published by Springer Science & Business Media. This book was released on 2004-04-13 with total page 190 pages. Available in PDF, EPUB and Kindle. Book excerpt: The continuous-time portfolio problem consists of finding the optimal investment strategy of an investor. In the classical Merton problem the investor can allocate his funds to a riskless savings account and risky assets. However, to get explicit results, it is assumed that the interest rates are deterministic and that the assets are default free. In this monograph both assumptions are weakened: The author analyzes and solves portfolio problems with stochastic interest rates and with defaultable assets. Besides, he briefly discusses how portfolio problems with foreign assets can be handled. The focus of the monograph is twofold: On the one hand, the economical problems are carefully explained, on the other hand their formal solution is rigorously presented. For this reason the text should be of interest to researchers with a Finance background as well as to researchers with a more formal background who would like to see how mathematics is applied to portfolio theory. TOC:Preliminaries from Stochastics.- Optimal Portfolios with Stochastic Interest Rates.- Elasticity Approach to Portfolio Optimization.- Barrier Derivatives with Curved Boundaries.- Optimal Portfolios with Dafaultable Assets - A Firm Value Approach.- References.- Abbreviations.- Notations.
Book Synopsis Optimal Investment Policy for Insurers Under the Constant Elasticity of Variance Model by : Xiaotao Liu
Download or read book Optimal Investment Policy for Insurers Under the Constant Elasticity of Variance Model written by Xiaotao Liu and published by . This book was released on 2018 with total page 21 pages. Available in PDF, EPUB and Kindle. Book excerpt: We solve in explicit form the optimal portfolio choice problem for an insurer with negative exponential utility over terminal wealth under the constant elasticity of variance (CEV) price model. The surplus process is assumed to follow a Brownian motion with drift and whose risk is correlated with the Brownian motion driving the risky assets. We first derive the corresponding Hamilton-Jacobi-Bellman (HJB) equation, and then simplify it into two parabolic partial differential equations (PDEs) via the variable change techniques. Finally, by the Feynman-Kac formula we solve the two PDEs and obtain the explicit solution of value function as well as the optimal investment policy. We identify four independent components of the optimal investment policy: the myopic, dynamic, static, and delta hedging demands. Previous literature, besides the myopic investment demands, in contrast, only determines either dynamic or static hedge demands, but not the both, not to mention the delta hedge demands. The delta hedging demands can be expressed as integrals of confluent hypergeometric function. We demonstrate that the static hedging demands are to hedge against the hedgeable risk of the surplus and the delta hedging demands further help to reduce the time-varying risk of the static hedged surplus process. Asymptotic analysis shows that as the variance elasticity parameter approaches to zero, both the dynamic and delta hedging demands vanish.
Book Synopsis Optimal Dynamic Investment Policies of a Value Maximizing Firm by : Peter M. Kort
Download or read book Optimal Dynamic Investment Policies of a Value Maximizing Firm written by Peter M. Kort and published by Springer. This book was released on 1989-05-10 with total page 200 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a contribution to the area of dynamic models of the firm. In Chapter 1, a general investment decision rule based on the concept of net present value of marginal investment is developed. In chapter 2, the rule is applied in deterministic dynamic models of the firm. This rule can be expressed as follows: If the net present value of marginal investment is positive, it is optimal for the firm to grow as fast as possible; If the net present value of marginal investment is zero, the firm is in its optimal situation and it determines its investment policy to maintain this position; If the net present value of marginal investment is negative, it is optimal for the firm to contract as much as possible. In Chapter 3, the influence of adjustment costs of investment on optimal dynamic firm behaviour is studied. To that end, models with convex and concave adjustment cost functions are developed and analysed by using the investment decision rule described above. In Chapter 4, the stochastic dynamic theory of the firm is extended by connecting it with the Intertemporal Capital Asset Pricing Model (ICAPM) developed by Merton.
Book Synopsis The Fair Value of Insurance Business by : Irwin T. Vanderhoof
Download or read book The Fair Value of Insurance Business written by Irwin T. Vanderhoof and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 327 pages. Available in PDF, EPUB and Kindle. Book excerpt: Insurance companies, as well as banks and thrift institutions, have traditionally reported assets and liabilities on the basis of their amortized cost, or book value. But following the turmoil in securities markets due to highly volatile interest rate fluctuations in the 1980s and the early 1990s, and problems caused by inadequate liquidity, in the mid-1990s the Financial Accounting Standards Board (FASB) issued a new ruling calling for financial intermediaries to report the fair, or market, value of most assets. Called FAS 115, this new standard is the first step in the eventual change to valuing all the assets and liabilities belonging to financial intermediaries under the fair value accounting method. Thus, these changes will pose tremendous future implications for three key business measures of a financial intermediary: Solvency: if the fair values of assets and liabilities are out-of-step, then healthy companies may report negative net worth and insolvent companies may appear to be in sound financial condition. Reported Earnings: if the fair values of assets and liabilities are out of step, then reported earnings will not accurately represent the financial operations of the company. Risk Management: FASB recently postponed the implementation of its new rules on accounting for the use of derivatives instruments. However, if the final set of rules for figuring the fair value of derivatives is not carefully crafted, it may be possible that companies prudently hedging their risks are subject to penalties in their financial reports, while companies taking greater risks appear to have less volatile financial performance. Compared to banks and other financial intermediaries, life insurance companies have the longest term and most complex liabilities, and hence the new FASB requirement poses the most severe challenges to the life insurance industry. The lessons learned from the debate among life insurance academics and professionals about how respond to the fair value reporting rule will be instructive to their counterparts in other sectors of the insurance industry, as well as those involved with other financial institutions. Of particular note are the two papers which comprise Part III. The first provides examples of the fair valuing of annuity contracts, while the second offers examples of the fair valuing of term insurance products. As the papers collected in The Fair Value of Insurance Business extend and update some of the issues treated in a previous Salomon Center conference volume, The Fair Value of Insurance Liabilities, this new volume may be viewed as a companion to the earlier book.
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 Insurance Company Investment Management Handbook by : Edmund A. Mennis
Download or read book Insurance Company Investment Management Handbook written by Edmund A. Mennis and published by . This book was released on 1992 with total page 680 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis A Decision Theoretic Approach to Optimal Investment Decisions and an Optimal Financial Structure Under Risk by : Franz Josef Sosnowski
Download or read book A Decision Theoretic Approach to Optimal Investment Decisions and an Optimal Financial Structure Under Risk written by Franz Josef Sosnowski and published by . This book was released on 1971 with total page 518 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Financial Management of Life Insurance Companies by : J. David Cummins
Download or read book Financial Management of Life Insurance Companies written by J. David Cummins and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 198 pages. Available in PDF, EPUB and Kindle. Book excerpt: th This book is published to commemorate the 50 Anniversary of the S.S. Huebner Foundation for Insurance Education. Administered at the Wharton School of the University of Pennsylvania, the Huebner Foundation was established in 1941 to strengthen insurance education at the collegiate level by increasing the number of professors specializing in insurance and enriching the literature in the field. The financial support of leading life insurance companies has enabled the Foundation to provide post-graduate education for prospective insurance teachers and scholars. Through its fellowship program, the Foundation supports students in the Ph.D. program in Risk and Insurance at the Wharton School. The success of the Foundation is measured by the accomplishments of its alumni. Former Huebner Fellows play leading roles in every major area of insurance education. Fellows teach insurance to tens of thousands of undergraduate and MBA students each year and have written hundreds of books and thousands of articles on insurance. Fellows hold leadership positions at the American College, the Life Office Management Association, and the Certified Employee Benefit Specialist Program. The Foundation was created in honor of Dr. Solomon S. Huebner, a pioneer in insurance education. Dr. Huebner taught the first organized course on the economics of insurance ever offered at the collegiate level in 1904. An internationally recognized author and teacher, Dr. Huebner had a profound impact on both insurance education and the insurance industry. He served on the faculty of the Wharton School for more than nearly fifty years.
Book Synopsis Ruin Probabilities (2nd Edition) by : Soren Asmussen
Download or read book Ruin Probabilities (2nd Edition) written by Soren Asmussen and published by World Scientific. This book was released on 2010-09-09 with total page 621 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book gives a comprehensive treatment of the classical and modern ruin probability theory. Some of the topics are Lundberg's inequality, the Cramér-Lundberg approximation, exact solutions, other approximations (e.g., for heavy-tailed claim size distributions), finite horizon ruin probabilities, extensions of the classical compound Poisson model to allow for reserve-dependent premiums, Markov-modulation, periodicity, change of measure techniques, phase-type distributions as a computational vehicle and the connection to other applied probability areas, like queueing theory. In this substantially updated and extended second version, new topics include stochastic control, fluctuation theory for Levy processes, Gerber-Shiu functions and dependence.
Book Synopsis Dynamic Portfolio Insurance and Equilibrium Pricing by : Zhongquan Zhou
Download or read book Dynamic Portfolio Insurance and Equilibrium Pricing written by Zhongquan Zhou and published by . This book was released on 1993 with total page 240 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Optimal Surrender and Asset Allocation Strategies for Equity-indexed Insurance Investors by : Wenxia Li
Download or read book Optimal Surrender and Asset Allocation Strategies for Equity-indexed Insurance Investors written by Wenxia Li and published by . This book was released on 2010 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Equity-indexed annuity (EIA) products are becoming more and more popular since they were first introduced in 1995. The growing popularity stems from the fact that the EIAs allow investors to earn part or all the equity accumulated and enjoy a minimum guaranteed growth rate on the principal. An EIA investor may consider surrendering the contract before maturity and invest in the stock index in order to earn the full stock growth. He may also invest in a risk-free asset for protection from downside risk. We consider an EIA policyholder who seeks the optimal surrender strategy, and asset allocation strategy after surrender, in order to maximize his expected discounted utility at expiration of the contract that is either the maturity or his time of death, whichever comes first. We derive the Hamilton-Jacobi-Bellman equations, satisfied by the optimal value function, and derive the optimal strategies. We find that the optimal surrender strategies appear in the form of a continuation region or two surrender boundaries. That is, the investor stays in the contract when the contract value is within the region. We also study the impact of product features, market assumptions and individual behavior patterns on the surrender boundaries.
Book Synopsis On the Lack of Participating Policy Usage by Stock Insurance Companies by : Geoffrey C. Friesen
Download or read book On the Lack of Participating Policy Usage by Stock Insurance Companies written by Geoffrey C. Friesen and published by . This book was released on 2006 with total page 31 pages. Available in PDF, EPUB and Kindle. Book excerpt: Stock insurers can reduce or eliminate agency conflicts between policyholders and stockholders by issuing participating insurance. Despite this benefit, most stock companies don't offer participating contracts. This study explains why. We study an equilibrium with both stock and mutual insurers in which stockholders set premiums to provide a fair expected return on their investment, and with a policyholder who chooses the insurance contract that maximizes her expected utility. We demonstrate that stockholders cannot profitably offer fully-participating contracts, but can profitably offer partially-participating insurance. However, when the policyholder participation fraction is high, the fair-return premium is so large that the policyholder always prefers fully participating insurance from the mutual company. Policies with lower levels of policyholder participation are optimal for policyholders with relatively high risk aversion, though such policies are usually prohibited by insurance legislation. Thus, the reason stock insurers rarely issue participating contracts isn't because the potential benefits are small or unimportant. Rather, profitability or regulatory constraints simply prevent stock insurers from exercising those benefits in equilibrium.
