OPTIMAL PROPORTIONAL REINSURANCE AND INVESTMENT PROBLEM WITH CONSTRAINTS ON RISK CONTROL IN A GENERAL JUMP-DIFFUSION FINANCIAL MARKET

We study the optimal proportional reinsurance and investment problem in a general jump-diffusion financial market. Assuming that the insurer’s surplus process follows a jump-diffusion process, the insurer can purchase proportional reinsurance from the reinsurer and invest in a risk-free asset and a risky asset, whose price is modelled by a general jump-diffusion process. The insurance company wishes to maximize the expected exponential utility of the terminal wealth. By using techniques of stochastic control theory, closed-form expressions for the value function and optimal strategy are obtained. A Monte Carlo simulation is conducted to illustrate that the closed-form expressions we derived are indeed the optimal strategies, and some numerical examples are presented to analyse the impact of model parameters on the optimal strategies.

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Jump Diffusion Models for Risky Debts: Quality Spread Differentials

International Journal of Theoretical and Applied Finance ◽

10.1142/s0219024903002158 ◽

2003 ◽

Vol 06 (06) ◽

pp. 655-662 ◽

Cited By ~ 1

Author(s):

Hoi Ying Wong ◽

Yue Kuen Kwok

Keyword(s):

Diffusion Process ◽

Closed Form ◽

Firm Value ◽

Jump Diffusion ◽

Brownian Diffusion ◽

Fixed Rate ◽

Floating Rate ◽

The Difference ◽

The Impact ◽

Risky Debt

The quality spread differential is defined to be the difference between the default premiums demanded for fixed rate and floating rate risky debts. The risky debt model based on Merton's firm value approach is used to examine the behaviors of the quality spread differential of fixed rate and floating rate debts. We extend earlier result by adopting Geometric Brownian diffusion process with jumps for the underlying firm value process of the debt issuer. Closed form formulas are obtained for the default premiums for risky debts. The impact of the jumps on the fixed-floating spread differential is examined.

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Optimal Reinsurance-Investment Problem for an Insurer and a Reinsurer with Jump-Diffusion Process

Discrete Dynamics in Nature and Society ◽

10.1155/2018/9424908 ◽

2018 ◽

Vol 2018 ◽

pp. 1-12

Author(s):

Hanlei Hu ◽

Zheng Yin ◽

Xiujuan Gao

Keyword(s):

Diffusion Process ◽

Optimal Strategies ◽

Jump Diffusion ◽

Sensitivity Analyses ◽

Programming Approach ◽

Investment Strategies ◽

Optimal Reinsurance ◽

Bellman Equations ◽

Dynamic Programming Approach ◽

Jump Diffusion Process

The optimal reinsurance-investment strategies considering the interests of both the insurer and reinsurer are investigated. The surplus process is assumed to follow a jump-diffusion process and the insurer is permitted to purchase proportional reinsurance from the reinsurer. Applying dynamic programming approach and dual theory, the corresponding Hamilton-Jacobi-Bellman equations are derived and the optimal strategies for exponential utility function are obtained. In addition, several sensitivity analyses and numerical illustrations in the case with exponential claiming distributions are presented to analyze the effects of parameters about the optimal strategies.

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OPTIMAL PROPORTIONAL REINSURANCE UNDER TWO CRITERIA: MAXIMIZING THE EXPECTED UTILITY AND MINIMIZING THE VALUE AT RISK

The ANZIAM Journal ◽

10.1017/s1446181110000878 ◽

2010 ◽

Vol 51 (4) ◽

pp. 449-463 ◽

Cited By ~ 3

Author(s):

ZHIBIN LIANG ◽

JUNYI GUO

Keyword(s):

At Risk ◽

Expected Utility ◽

Value At Risk ◽

Optimal Solution ◽

Optimal Strategies ◽

Pareto Optimal Solution ◽

Model Parameters ◽

Pareto Optimal ◽

Proportional Reinsurance ◽

The Impact

AbstractWe consider the optimal proportional reinsurance from an insurer’s point of view to maximize the expected utility and minimize the value at risk. Under the general premium principle, we prove the existence and uniqueness of the optimal strategies and Pareto optimal solution, and give the relationship between the optimal strategies. Furthermore, we study the optimization problem with the variance premium principle. When the total claim sizes are normally distributed, explicit expressions for the optimal strategies and Pareto optimal solution are obtained. Finally, some numerical examples are presented to show the impact of the major model parameters on the optimal results.

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