Optimal Reinsurance-Investment Problem for an Insurer and a Reinsurer with 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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An Optimal Portfolio Problem of DC Pension with Input-Delay and Jump-Diffusion Process

Mathematical Problems in Engineering ◽

10.1155/2020/4343629 ◽

2020 ◽

Vol 2020 ◽

pp. 1-9

Author(s):

Weixiang Xu ◽

Jinggui Gao

Keyword(s):

Diffusion Process ◽

Control Problem ◽

Jump Diffusion ◽

Investment Strategy ◽

Optimal Portfolio ◽

Input Delay ◽

Programming Approach ◽

Time Interval ◽

Stochastic Dynamic ◽

Jump Diffusion Process

In this paper, an optimal portfolio control problem of DC pension is studied where the time interval between the implementation of investment behavior and its effectiveness (hereafter input-delay) is particularly focused. There are two assets available for investment: a risk-free cash bond and a risky stock with a jump-diffusion process. And the wealth process of the pension fund is modeled as a stochastic delay differential equation. To secure a comfortable retirement life for pension members and also avoid excessive risk, the fund managers in this paper aim to minimize the expected value of quadratic deviations between the actual terminal fund scale and a preset terminal target. By applying the stochastic dynamic programming approach and the match method, the optimal portfolio control problem is solved and the closed-form solution is obtained. In addition, an algorithm is developed to calculate the numerical solution of the optimal strategy. Finally, we have performed a sensitivity analysis to explore how the managers’ preset terminal target, the length of input-delay, and the jump intensity of risky assets affect the optimal investment strategy.

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

The ANZIAM Journal ◽

10.1017/s1446181115000280 ◽

2016 ◽

Vol 57 (3) ◽

pp. 352-368

Author(s):

HUIMING ZHU ◽

YA HUANG ◽

JIEMING ZHOU ◽

XIANGQUN YANG ◽

CHAO DENG

Keyword(s):

Diffusion Process ◽

Closed Form ◽

Financial Market ◽

Optimal Strategies ◽

Jump Diffusion ◽

Model Parameters ◽

Proportional Reinsurance ◽

Investment Problem ◽

Jump Diffusion Process ◽

The Impact

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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