scholarly journals Optimal Reinsurance-Investment Problem under Mean-Variance Criterion with n Risky Assets

2020 ◽  
Vol 2020 ◽  
pp. 1-16
Author(s):  
Peng Yang
Keyword(s):  
Financial Market ◽  
Investment Strategy ◽  
Hjb Equation ◽  
Model Parameters ◽  
Optimal Reinsurance ◽  
Risky Assets ◽  
Terminal Wealth ◽  
Investment Problem ◽  
Mean Variance ◽  
Variance Criterion

Based on the mean-variance criterion, this paper investigates the continuous-time reinsurance and investment problem. The insurer’s surplus process is assumed to follow Cramér–Lundberg model. The insurer is allowed to purchase reinsurance for reducing claim risk. The reinsurance pattern that the insurer adopts is combining proportional and excess of loss reinsurance. In addition, the insurer can invest in financial market to increase his wealth. The financial market consists of one risk-free asset and n correlated risky assets. The objective is to minimize the variance of the terminal wealth under the given expected value of the terminal wealth. By applying the principle of dynamic programming, we establish a Hamilton–Jacobi–Bellman (HJB) equation. Furthermore, we derive the explicit solutions for the optimal reinsurance-investment strategy and the corresponding efficient frontier by solving the HJB equation. Finally, numerical examples are provided to illustrate how the optimal reinsurance-investment strategy changes with model parameters.

Worst-Case Investment Strategy with Delay

2018 ◽  
Vol 6 (1) ◽  
pp. 35-57
Author(s):  
Chunxiang A ◽  
Yi Shao
Keyword(s):  
Financial Market ◽  
Normal State ◽  
Optimal Investment ◽  
Investment Strategy ◽  
Model Parameters ◽  
Investment Strategies ◽  
Case Scenario ◽  
Worst Case ◽  
Risky Assets ◽  
Investment Optimization

AbstractThis paper considers a worst-case investment optimization problem with delay for a fund manager who is in a crash-threatened financial market. Driven by existing of capital inflow/outflow related to history performance, we investigate the optimal investment strategies under the worst-case scenario and the stochastic control framework with delay. The financial market is assumed to be either in a normal state (crash-free) or in a crash state. In the normal state the prices of risky assets behave as geometric Brownian motion, and in the crash state the prices of risky assets suddenly drop by a certain relative amount, which induces to a dropping of the total wealth relative to that of crash-free state. We obtain the ordinary differential equations satisfied by the optimal investment strategies and the optimal value functions under the power and exponential utilities, respectively. Finally, a numerical simulation is provided to illustrate the sensitivity of the optimal strategies with respective to the model parameters.

scholarly journals Robust Time-Consistent Portfolio Selection for an Investor under CEV Model with Inflation Influence

2020 ◽  
Vol 2020 ◽  
pp. 1-14
Author(s):  
Peng Yang
Keyword(s):  
Probability Measure ◽  
Financial Market ◽  
Optimal Investment ◽  
Investment Strategy ◽  
Risky Asset ◽  
Control Technique ◽  
Model Parameters ◽  
Cev Model ◽  
Terminal Wealth ◽  
Optimal Investment Strategy

A robust time-consistent optimal investment strategy selection problem under inflation influence is investigated in this article. The investor may invest his wealth in a financial market, with the aim of increasing wealth. The financial market includes one risk-free asset, one risky asset, and one inflation-indexed bond. The price process of the risky asset is governed by a constant elasticity of variance (CEV) model. The investor is ambiguity-averse; he doubts about the model setting under the original probability measure. To dispel this concern, he seeks a set of alternative probability measures, which are absolutely continuous to the original probability measure. The objective of the investor is to seek a time-consistent strategy so as to maximize his expected terminal wealth meanwhile minimizing his variance of the terminal wealth in the worst-case scenario. By using the stochastic optimal control technique, we derive closed-form solutions for the optimal time-consistent investment strategy, the probability scenario, and the value function. Finally, the influences of model parameters on the optimal investment strategy and utility loss function are examined through numerical experiments.

scholarly journals Equilibrium reinsurance-investment strategy with a common shock under two kinds of premium principles

2021 ◽  
Author(s):  
Junna Bi ◽  
Danping Li ◽  
Nan Zhang
Keyword(s):  
Investment Strategy ◽  
Expected Value ◽  
Value Premium ◽  
Equilibrium Strategy ◽  
Model Parameters ◽  
Optimal Reinsurance ◽  
Investment Problem ◽  
Common Shock ◽  
Game Theoretic ◽  
Hamilton Jacobi Bellman

This paper investigates the optimal mean-variance reinsurance-investment problem for an insurer with a common shock dependence under two kinds of popular premium principles: the variance premium principle and the expected value premium principle. We formulate the optimization problem within a game theoretic framework and derive the closed-form expressions of the equilibrium reinsurance-investment strategy and equilibrium value function under the two different premium principles by solving the extended Hamilton-Jacobi-Bellman system of equations. We find that under the variance premium principle, the proportional reinsurance is the optimal reinsurance strategy for the optimal reinsurance-investment problem with a common shock, while under the expected value premium principle, the excess-of-loss reinsurance is the optimal reinsurance strategy. In addition, we illustrate the equilibrium reinsurance-investment strategy by numerical examples and discuss the impacts of model parameters on the equilibrium strategy.

scholarly journals Closed-Loop Equilibrium Reinsurance-Investment Strategy with Insider Information and Default Risk

2021 ◽  
Vol 2021 ◽  
pp. 1-32
Author(s):  
Peng Yang
Keyword(s):  
Financial Market ◽  
Default Risk ◽  
Closed Loop ◽  
Investment Strategy ◽  
Model Parameters ◽  
Hjb Equations ◽  
Loop Control ◽  
Insider Information ◽  
Control Approach ◽  
Terminal Wealth

This paper studies the closed-loop equilibrium reinsurance-investment problem with insider information and default risk. The financial market consists of one risky asset, one defaultable bond, and one risk-free asset. The surplus process is governed by a jump-diffusion process. Two kinds of dependencies between the insurance market and the financial market are considered. In addition, the insurer has some extra claims information available from the beginning of the trading interval. The objective of the insurer is to choose a time-consistent reinsurance-investment strategy so as to maximize the expected terminal wealth while minimizing the variance of the terminal wealth. Since this problem is time-inconsistent, using closed-loop control approach from the perspective of game theory, we establish the extended Hamilton–Jacobi–Bellman (HJB) equations for the postdefault case and the predefault case, respectively. Closed-form solutions for the closed-loop equilibrium reinsurance-investment strategy and the corresponding value function are obtained. Finally, we provide a series of numerical examples to illustrate the effects of insider information and other some important model parameters on the closed-loop equilibrium reinsurance and investment strategies. The result analyses reveal some interesting phenomena and provide useful guidances for reinsurance and investment in reality.

Mean-variance equilibrium asset-liability management strategy with cointegrated assets

2021 ◽  
Vol 62 ◽  
pp. 209-234
Author(s):  
Mei Choi Chiu
Keyword(s):  
Financial Market ◽  
Time Consistency ◽  
Time Inconsistency ◽  
Asset Liability Management ◽  
Risky Assets ◽  
Liability Management ◽  
Equilibrium Control ◽  
Management Problems ◽  
Hamilton Jacobi Bellman ◽  
Mean Variance

This paper investigates asset-liability management problems in a continuous-time economy. When the financial market consists of cointegrated risky assets, institutional investors attempt to make profit from the cointegration feature on the one hand, while on the other hand they need to maintain a stable surplus level, that is, the company’s wealth less its liability. Challenges occur when the liability is random and cannot be fully financed or hedged through the financial market. For mean–variance investors, an additional concern is the rational time-consistency issue, which ensures that a decision made in the future will not be restricted by the current surplus level. By putting all these factors together, this paper derives a closed-form feedback equilibrium control for time-consistent mean–variance asset-liability management problems with cointegrated risky assets. The solution is built upon the Hamilton–Jacobi–Bellman framework addressing time inconsistency. doi: 10.1017/S1446181120000164

scholarly journals Robust Optimal Excess-of-Loss Reinsurance and Investment Problem with Delay and Dependent Risks

2019 ◽  
Vol 2019 ◽  
pp. 1-21
Author(s):  
Yan Zhang ◽  
Peibiao Zhao
Keyword(s):  
Investment Strategy ◽  
Risky Asset ◽  
Exponential Utility ◽  
Heston Model ◽  
Verification Theorem ◽  
Terminal Wealth ◽  
Investment Problem ◽  
Dependent Risks ◽  
Insurance Business ◽  
Explicit Expressions

This paper investigates a robust optimal excess-of-loss reinsurance and investment problem with delay and dependent risks for an ambiguity-averse insurer (AAI). The AAI’s wealth process is assumed to be two dependent classes of insurance business. He/she can purchase excess-of-loss reinsurance from the reinsurer and invest in a risk-free asset and a risky asset whose price follows Heston model. We obtain the explicit expressions of the optimal excess-of-loss reinsurance and investment strategy by maximizing the expected exponential utility of AAI’s terminal wealth. Finally, we give the proof of the verification theorem. Our models and results posed here can be regarded as a generalization of the existing results in the literature.

A time consistent derivative strategy

2020 ◽  
Vol 07 (01) ◽  
pp. 2050004
Author(s):  
Walter Mudzimbabwe
Keyword(s):  
Nash Equilibrium ◽  
Utility Function ◽  
Stochastic Volatility ◽  
Efficient Frontier ◽  
Equation System ◽  
Investment Strategy ◽  
Hjb Equation ◽  
Game Theoretic ◽  
Time Inconsistent ◽  
Mean Variance

In this paper, we derive a time consistent investment strategy for an investor who can invest not only in a bond and stock but in a derivative as well. In order to capture typical features shown by stocks, the stock and by extension the derivative depends on stochastic volatility. We assume that the investor is interested in maximizing a mean–variance utility function. Since the problem is time-inconsistent, we formulate the problem in game theoretic way and seek a subgame Nash equilibrium as the strategy. By solving an extended HJB equation system, we derive explicit time-consistent strategy and the corresponding efficient frontier. In order to show efficiency of the derivative strategy, we compare it with a strategy for the case of a market without a derivative. Our results show that efficient frontier for an investor with a derivative is higher than without derivative.

scholarly journals Time-Consistent Investment and Reinsurance Strategies for Mean-Variance Insurers under Stochastic Interest Rate and Stochastic Volatility

Mathematics ◽  
2020 ◽  
Vol 8 (12) ◽  
pp. 2183
Author(s):  
Jiaqi Zhu ◽  
Shenghong Li
Keyword(s):  
Interest Rate ◽  
Stochastic Volatility ◽  
Financial Market ◽  
Equilibrium Strategy ◽  
Stochastic Interest Rate ◽  
Programming Approach ◽  
Model Parameters ◽  
Stochastic Interest ◽  
The Impact ◽  
Mean Variance

This paper studies the time-consistent optimal investment and reinsurance problem for mean-variance insurers when considering both stochastic interest rate and stochastic volatility in the financial market. The insurers are allowed to transfer insurance risk by proportional reinsurance or acquiring new business, and the jump-diffusion process models the surplus process. The financial market consists of a risk-free asset, a bond, and a stock modelled by Heston’s stochastic volatility model. Interest rate in the market is modelled by the Vasicek model. By using extended dynamic programming approach, we explicitly derive equilibrium reinsurance-investment strategies and value functions. In addition, we provide and prove a verification theorem and then prove the solution we get satisfies it. Moreover, sensitive analysis is given to show the impact of several model parameters on equilibrium strategy and the efficient frontier.

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