Robust Optimal Investment-Reinsurance Strategies for a Jump-Diffusion Risk Model with Mean-reverting Stock Return

2021 ◽  
Vol 7 (6) ◽  
pp. 6100-6114
Author(s):  
Wu Yungao
Keyword(s):  
Financial Market ◽  
Stock Return ◽  
Value Function ◽  
Risk Model ◽  
Optimal Investment ◽  
Jump Diffusion ◽  
Insurance Companies ◽  
Insurance Company ◽  
Terminal Time ◽  
The Value Function

Objectives: This paper proposes a strategy of robust optimal investment reinsurance for insurance companies. It was assumed that the surplus procedure of the insurance company satisfies the jump-diffusion procedure. Insurance companies could invest their surplus funds in the financial market consisted of both risk assets and one risk-free asset. The price procedure of risk assets satisfies the stochastic procedure with a mean reversion rate. Considering the uncertainty of the model, the ambiguity-averse insurance firm aims to enhance the exponential utility of insurance surplus at terminal time. This paper has investigated the problem of robust optimal investment reinsurance and obtained the differential equation supported by the value function.

scholarly journals OPTIMAL INVESTMENT AND REINSURANCE IN A JUMP DIFFUSION RISK MODEL

2011 ◽  
Vol 52 (3) ◽  
pp. 250-262 ◽  
Author(s):  
XIANG LIN ◽  
PENG YANG
Keyword(s):  
Risk Model ◽  
Optimal Investment ◽  
Jump Diffusion ◽  
Risk Process ◽  
Proportional Reinsurance ◽  
Insurance Company ◽  
Closed Form Solutions ◽  
Hamilton Jacobi Bellman Equation ◽  
Hamilton Jacobi Bellman ◽  
The Value Function

AbstractWe consider an insurance company whose surplus is governed by a jump diffusion risk process. The insurance company can purchase proportional reinsurance for claims and invest its surplus in a risk-free asset and a risky asset whose return follows a jump diffusion process. Our main goal is to find an optimal investment and proportional reinsurance policy which maximizes the expected exponential utility of the terminal wealth. By solving the corresponding Hamilton–Jacobi–Bellman equation, closed-form solutions for the value function as well as the optimal investment and proportional reinsurance policy are obtained. We also discuss the effects of parameters on the optimal investment and proportional reinsurance policy by numerical calculations.

scholarly journals Optimal per-loss reinsurance and investment to minimize the probability of drawdown

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Xia Han ◽  
Zhibin Liang ◽  
Yu Yuan ◽  
Caibin Zhang
Keyword(s):  
Closed Form ◽  
Financial Market ◽  
Value Function ◽  
Risk Model ◽  
Investment Strategy ◽  
Insurance Company ◽  
Optimal Reinsurance ◽  
Claim Number ◽  
Common Shock ◽  
Insurance Business

<p style='text-indent:20px;'>In this paper, we study an optimal reinsurance-investment problem in a risk model with two dependent classes of insurance business, where the two claim number processes are correlated through a common shock component. We assume that the insurer can purchase per-loss reinsurance for each line of business and invest its surplus in a financial market consisting of a risk-free asset and a risky asset. Under the criterion of minimizing the probability of drawdown, the closed-form expressions for the optimal reinsurance-investment strategy and the corresponding value function are obtained. We show that the optimal reinsurance strategy is in the form of pure excess-of-loss reinsurance strategy under the expected value principle, and under the variance premium principle, the optimal reinsurance strategy is in the form of pure quota-share reinsurance. Furthermore, we extend our model to the case where the insurance company involves <inline-formula><tex-math id="M1">\begin{document}$ n $\end{document}</tex-math></inline-formula> <inline-formula><tex-math id="M2">\begin{document}$ (n\geq3) $\end{document}</tex-math></inline-formula> dependent classes of insurance business and the optimal results are derived explicitly as well.</p>

scholarly journals EVOLUTION OF AMERICAN OPTION VALUE FUNCTION ON A DIVIDEND PAYING STOCK UNDER JUMP-DIFFUSION PROCESSES

2017 ◽  
Vol 2 (3) ◽  
pp. 212-221
Author(s):  
Рехман ◽  
Nazir Rekhman ◽  
Хуссейн ◽  
Zakir Khusseyn ◽  
Али ◽  
...  
Keyword(s):  
Variational Inequalities ◽  
Value Function ◽  
Diffusion Processes ◽  
Equivalent Form ◽  
Jump Diffusion ◽  
American Option ◽  
Option Value ◽  
Jump Diffusion Processes ◽  
Hedging Strategies ◽  
The Value Function

This work is devoted to the analysis and evolution of the value function of American type options on a dividend paying stock under jump diffusion processes. An equivalent form of the value function is obtained and analyzed. Moreover, variational inequalities satisfied by this function are investigated. These results can be used to investigate the optimal hedging strategies and optimal exercise boundaries of the corresponding options.

scholarly journals A Simulation Approach to Statistical Estimation of Multiperiod Optimal Portfolios

2012 ◽  
Vol 2012 ◽  
pp. 1-13
Author(s):  
Hiroshi Shiraishi
Keyword(s):  
Portfolio Choice ◽  
Value Function ◽  
Sample Path ◽  
Optimal Investment ◽  
Investment Strategy ◽  
Time Dependency ◽  
Portfolio Rebalancing ◽  
Sample Paths ◽  
Optimal Investment Strategy ◽  
The Value Function

This paper discusses a simulation-based method for solving discrete-time multiperiod portfolio choice problems under AR(1) process. The method is applicable even if the distributions of return processes are unknown. We first generate simulation sample paths of the random returns by using AR bootstrap. Then, for each sample path and each investment time, we obtain an optimal portfolio estimator, which optimizes a constant relative risk aversion (CRRA) utility function. When an investor considers an optimal investment strategy with portfolio rebalancing, it is convenient to introduce a value function. The most important difference between single-period portfolio choice problems and multiperiod ones is that the value function is time dependent. Our method takes care of the time dependency by using bootstrapped sample paths. Numerical studies are provided to examine the validity of our method. The result shows the necessity to take care of the time dependency of the value function.

تقييم الأداء المالي لشركات التامين في دولة قطر باستخدام DUPONT SYSTEM

2021 ◽  
Vol 2020 (67) ◽  
pp. 29-50
Author(s):  
م. كفاح جبار حسن
Keyword(s):  
Optimal Investment ◽  
Profit Margin ◽  
Insurance Companies ◽  
Insurance Company ◽  
Financial Leverage ◽  
Return On Equity ◽  
Differentiation Strategy ◽  
Leadership Strategy ◽  
Utility Index ◽  
Cost Leadership Strategy

The study of the mutual relationship between return and risk is prepared by the DUPONT SYSTEM for a period of 10 years from 2008 to 2017 in Qatari insurance companies. Costs, which characterized the Qatar General Insurance Company by achieving the highest average profit margin of 99,699 and the AU Asset Utility Index, which measures the efficiency of management in using its assets to achieve its revenues, which characterized Doha Insurance Company as it achieved the highest asset benefit of 34,771 Financial leverage EM, or the so-called ownership multiplier index, which is the ratio that measures the risks related to the use of ownership money, which characterized Qatar Insurance Company, as it achieved the highest rate of raising money of 267,677. The aim of using DUPONT SYSTEM is to compare the performance of companies in the same industry as network analysis to predict future changes, thus adding another dimension to the evaluation of Qatari insurance companies for optimal investment based on sound performance evaluation. The results of the study showed that companies that follow the policy of cost leadership strategy may It achieved a lower return than that which followed the policy of differentiation strategy. The research hypotheses were tested using ANOVA, and the following was found: 1- The existence of statistically significant differences between Qatari companies operating in the insurance field due to the return on equity (ROE). 2- The existence of statistically significant differences between Qatari insurance companies due to the financial leverage index Equity On Multiplier (EM). 3- There are statistically significant differences between Qatari insurance companies attributable to the Return On Asset index (ROA). 4- There are statistically significant differences between Qatari insurance companies due to the Profit Margin (PM) indicator. To confirm the results, a Multiple Comparisons Tukey was performed

scholarly journals Optimal capital injections and dividends with tax in a risk model in discrete time

2020 ◽  
Vol 10 (1) ◽  
pp. 235-259
Author(s):  
Katharina Bata ◽  
Hanspeter Schmidli
Keyword(s):  
Discrete Time ◽  
Optimal Strategy ◽  
Bellman Equation ◽  
Value Function ◽  
Risk Model ◽  
Barrier Type ◽  
Optimal Capital ◽  
Capital Injections ◽  
The Value Function ◽  
Special Case

AbstractWe consider a risk model in discrete time with dividends and capital injections. The goal is to maximise the value of a dividend strategy. We show that the optimal strategy is of barrier type. That is, all capital above a certain threshold is paid as dividend. A second problem adds tax to the dividends but an injection leads to an exemption from tax. We show that the value function fulfils a Bellman equation. As a special case, we consider the case of premia of size one. In this case we show that the optimal strategy is a two barrier strategy. That is, there is a barrier if a next dividend of size one can be paid without tax and a barrier if the next dividend of size one will be taxed. In both models, we illustrate the findings by de Finetti’s example.

scholarly journals RUIN PROBABILITIES UNDER AN OPTIMAL INVESTMENT AND PROPORTIONAL REINSURANCE POLICY IN A JUMP DIFFUSION RISK PROCESS

2009 ◽  
Vol 51 (1) ◽  
pp. 34-48 ◽  
Author(s):  
YIPING QIAN ◽  
XIANG LIN
Keyword(s):  
Ruin Probability ◽  
Market Price ◽  
Optimal Investment ◽  
Jump Diffusion ◽  
Risk Process ◽  
Closed Form Expression ◽  
Proportional Reinsurance ◽  
Insurance Company ◽  
Risky Assets ◽  
Price Of Risk

AbstractIn this paper, we consider an insurance company whose surplus (reserve) is modeled by a jump diffusion risk process. The insurance company can invest part of its surplus in n risky assets and purchase proportional reinsurance for claims. Our main goal is to find an optimal investment and proportional reinsurance policy which minimizes the ruin probability. We apply stochastic control theory to solve this problem. We obtain the closed form expression for the minimal ruin probability, optimal investment and proportional reinsurance policy. We find that the minimal ruin probability satisfies the Lundberg equality. We also investigate the effects of the diffusion volatility parameter, the market price of risk and the correlation coefficient on the minimal ruin probability, optimal investment and proportional reinsurance policy through numerical calculations.

scholarly journals Dynamic Index Optimal Investment Strategy Based on Stochastic Differential Equations in Financial Market Options

2021 ◽  
Vol 2021 ◽  
pp. 1-9
Author(s):  
Jun Zhang
Keyword(s):  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Financial Market ◽  
Capital Investment ◽  
Optimal Investment ◽  
Investment Strategy ◽  
Insurance Companies ◽  
Investment Efficiency ◽  
Bank Deposits ◽  
Optimal Investment Strategy

With the gradual development and improvement of the financial market, financial derivatives such as futures and options have also become the objects of competition in the financial market. Therefore, how to make the most favorable and optimized investment and consumption when options are included? It has become a problem facing investors. Aiming at the optimal investment problem of investors, this paper studies the calculation of an optimal investment strategy in stochastic differential equations in financial market options on the basis of fuzzy theory. Now, stochastic calculus has become an important branch of stochastic analysis, finance, control, and other fields. The study of introducing stochastic differential equations is mainly to solve the stochastic control problem, which is the principle of the stochastic maximum. In finance, some hedging or pricing problems of contingent rights can eventually be transformed into a series of stochastic differential equations. Based on the historical data of five aspects of bank deposits, bonds, funds, stocks, and real estate of four listed insurance companies, the paper analyzes the optimization strategy of the capital investment of listed insurance companies based on the investment yield of the domestic investment market. According to the final results, the historical proportion of bank deposits of the superior company is 27%, and the optimal proportion given by the model is 25%; the total proportion of funds and stocks is 15%, and the optimal proportion of funds analyzed in the model is 20% and the optimal proportion of stocks is 10%. Therefore, the final results show that the investment efficiency of listed insurance companies can actually increase investment in stocks and funds and reduce the proportion of bank deposits to obtain greater investment returns.

scholarly journals The Absolute Ruin Insurance Risk Model with a Threshold Dividend Strategy

Symmetry ◽  
2018 ◽  
Vol 10 (9) ◽  
pp. 377 ◽  
Author(s):  
Wenguang Yu ◽  
Yujuan Huang ◽  
Chaoran Cui
Keyword(s):  
Risk Model ◽  
Insurance Companies ◽  
Insurance Company ◽  
Insurance Risk ◽  
Threshold Dividend Strategy ◽  
Dividend Payments ◽  
Absolute Ruin ◽  
The Absolute ◽  
Debit Interest ◽  
Insurance Risk Model

The absolute ruin insurance risk model is modified by including some valuable market economic information factors, such as credit interest, debit interest and dividend payments. Such information is especially important for insurance companies to control risks. We further assume that the insurance company is able to finance and continue to operate when its reserve is negative. We investigate the integro-differential equations for some interest actuarial diagnostics. We also provide numerical examples to explain the effects of relevant parameters on actuarial diagnostics.

Backward Stochastic PDE and Imperfect Hedging

2003 ◽  
Vol 06 (07) ◽  
pp. 663-692 ◽  
Author(s):  
M. Mania ◽  
R. Tevzadze
Keyword(s):  
Financial Market ◽  
Asset Prices ◽  
Random Function ◽  
Value Function ◽  
Market Model ◽  
Stochastic Pde ◽  
Continuous Semimartingale ◽  
Incomplete Financial Market ◽  
Mean Variance ◽  
The Value Function

We consider a problem of minimization of a hedging error, measured by a positive convex random function, in an incomplete financial market model, where the dynamics of asset prices is given by an Rd-valued continuous semimartingale. Under some regularity assumptions we derive a backward stochastic PDE for the value function of the problem and show that the strategy is optimal if and only if the corresponding wealth process satisfies a certain forward-SDE. As an example the case of mean-variance hedging is considered.

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