Non Zero Sum Stochastic Differential Reinsurance And Investment Games With Default Risk

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Non-Zero-Sum Stochastic Differential Reinsurance and Investment Games with Default Risk

Author : Chao Deng
Publisher :
ISBN 13 :
Total Pages : 32 pages
Book Rating : 4.:/5 (13 download)

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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.

Robust Non-Zero-Sum Stochastic Differential Investment-Reinsurance Game

Author : Chi Seng Pun
Publisher :
ISBN 13 :
Total Pages : 26 pages
Book Rating : 4.:/5 (13 download)

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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.

Non-Zero-Sum Stochastic Differential Reinsurance Game and Optimal Asset Allocation with Restriction on Liquidity

Author : Chuan Xu
Publisher :
ISBN 13 :
Total Pages : 96 pages
Book Rating : 4.:/5 (115 download)

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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:

Non-zero-sum Stochastic Differential Games for Asset-liability Management with Stochastic Inflation and Stochastic Volatility

Author : Yumo Zhang
Publisher :
ISBN 13 :
Total Pages : 0 pages
Book Rating : 4.:/5 (137 download)

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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.

Determining the Insurer's Optimal Investment and Reinsurance Strategy Based on Stochastic Differential Game

Author : Hong Mao
Publisher :
ISBN 13 :
Total Pages : 0 pages
Book Rating : 4.:/5 (137 download)

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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.

Dynamic Economic Problems with Regime Switches

Author : Josef L. Haunschmied
Publisher : Springer Nature
ISBN 13 : 3030545768
Total Pages : 317 pages
Book Rating : 4.0/5 (35 download)

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Book Synopsis Dynamic Economic Problems with Regime Switches by : Josef L. Haunschmied

Download or read book Dynamic Economic Problems with Regime Switches written by Josef L. Haunschmied and published by Springer Nature. This book was released on 2020-11-07 with total page 317 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents the state of the art in the relatively new field of dynamic economic modelling with regime switches. The contributions, written by prominent scholars in the field, focus on dynamic decision problems with regime changes in underlying dynamics or objectives. Such changes can be externally driven or internally induced by decisions. Utilising the most advanced mathematical methods in optimal control and dynamic game theory, the authors address a broad range of topics, including capital accumulation, innovations, financial decisions, population economics, environmental and resource economics, institutional change and the dynamics of addiction. Given its scope, the book will appeal to all scholars interested in mathematical and quantitative economics.

Time Inconsistent Stochastic Differential Game

Author : Hong Mao
Publisher :
ISBN 13 :
Total Pages : 35 pages
Book Rating : 4.:/5 (13 download)

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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.

Credit Risk

Author : Darrell Duffie
Publisher : Princeton University Press
ISBN 13 : 1400829178
Total Pages : 415 pages
Book Rating : 4.4/5 (8 download)

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Book Synopsis Credit Risk by : Darrell Duffie

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.

Optimal Portfolios with Stochastic Interest Rates and Defaultable Assets

Author : Holger Kraft
Publisher : Springer Science & Business Media
ISBN 13 : 9783540212300
Total Pages : 190 pages
Book Rating : 4.2/5 (123 download)

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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.

Aspects of Risk Theory

Author : Jan Grandell
Publisher : Springer Science & Business Media
ISBN 13 : 1461390583
Total Pages : 186 pages
Book Rating : 4.4/5 (613 download)

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Book Synopsis Aspects of Risk Theory by : Jan Grandell

Download or read book Aspects of Risk Theory written by Jan Grandell and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 186 pages. Available in PDF, EPUB and Kindle. Book excerpt: Risk theory, which deals with stochastic models of an insurance business, is a classical application of probability theory. The fundamental problem in risk theory is to investigate the ruin possibility of the risk business. Traditionally the occurrence of the claims is described by a Poisson process and the cost of the claims by a sequence of random variables. This book is a treatise of risk theory with emphasis on models where the occurrence of the claims is described by more general point processes than the Poisson process, such as renewal processes, Cox processes and general stationary point processes. In the Cox case the possibility of risk fluctuation is explicitly taken into account. The presentation is based on modern probabilistic methods rather than on analytic methods. The theory is accompanied with discussions on practical evaluation of ruin probabilities and statistical estimation. Many numerical illustrations of the results are given.

Risk Analysis and Portfolio Modelling

Author : Elisa Luciano
Publisher : MDPI
ISBN 13 : 3039216244
Total Pages : 224 pages
Book Rating : 4.0/5 (392 download)

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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.

Modern Actuarial Risk Theory

Author : Rob Kaas
Publisher : Springer Science & Business Media
ISBN 13 : 3540867368
Total Pages : 394 pages
Book Rating : 4.5/5 (48 download)

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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.

Ruin Probabilities

Author : S?ren Asmussen
Publisher : World Scientific
ISBN 13 : 9814282529
Total Pages : 621 pages
Book Rating : 4.8/5 (142 download)

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Book Synopsis Ruin Probabilities by : S?ren Asmussen

Download or read book Ruin Probabilities written by S?ren Asmussen and published by World Scientific. This book was released on 2010 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 Cramr?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.

How I Became a Quant

Author : Richard R. Lindsey
Publisher : John Wiley & Sons
ISBN 13 : 1118044754
Total Pages : 406 pages
Book Rating : 4.1/5 (18 download)

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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.

Mathematical Reviews

Author :
Publisher :
ISBN 13 :
Total Pages : 870 pages
Book Rating : 4.3/5 (91 download)

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Book Synopsis Mathematical Reviews by :

Download or read book Mathematical Reviews written by and published by . This book was released on 2003-05 with total page 870 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Reinsurance

Author : Hansjörg Albrecher
Publisher : John Wiley & Sons
ISBN 13 : 0470772689
Total Pages : 366 pages
Book Rating : 4.4/5 (77 download)

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Book Synopsis Reinsurance by : Hansjörg Albrecher

Download or read book Reinsurance written by Hansjörg Albrecher and published by John Wiley & Sons. This book was released on 2017-11-06 with total page 366 pages. Available in PDF, EPUB and Kindle. Book excerpt: Reinsurance: Actuarial and Statistical Aspects provides a survey of both the academic literature in the field as well as challenges appearing in reinsurance practice and puts the two in perspective. The book is written for researchers with an interest in reinsurance problems, for graduate students with a basic knowledge of probability and statistics as well as for reinsurance practitioners. The focus of the book is on modelling together with the statistical challenges that go along with it. The discussed statistical approaches are illustrated alongside six case studies of insurance loss data sets, ranging from MTPL over fire to storm and flood loss data. Some of the presented material also contains new results that have not yet been published in the research literature. An extensive bibliography provides readers with links for further study.

Applications of Stochastic Optimal Control to Economics and Finance

Author : Salvatore Federico
Publisher :
ISBN 13 : 9783039360581
Total Pages : 206 pages
Book Rating : 4.3/5 (65 download)

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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.