scholarly journals Open-loop equilibrium mean-variance reinsurance, new business and investment strategies with constraints

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Liming Zhang ◽  
Rongming Wang ◽  
Jiaqin Wei
Keyword(s):  
Convex Set ◽  
Investment Strategy ◽  
Open Loop ◽  
Equilibrium Strategy ◽  
Investment Strategies ◽  
Risky Investment ◽  
New Business ◽  
New Policies ◽  
Risk Processes ◽  
Mean Variance

<p style='text-indent:20px;'>In this paper, we study a general mean-variance reinsurance, new business and investment problem, where the claim processes of original and new businesses are modeled by two different risk processes and the safety loadings of reinsurance and new business are different. The retention level of the insurer is constrained in <inline-formula><tex-math id="M1">\begin{document}$ [0,1] $\end{document}</tex-math></inline-formula> and the controls of new business and risky investment are required to be non-negative. This model relaxes the limitations of those in existing research. By using the projection onto the convex set controls valued in, we obtain an open-loop equilibrium reinsurance-new business-investment strategy explicitly. We also show that the obtained equilibrium strategy is the optimal one among all deterministic strategies in the sense that it yields the smallest mean-variance cost. In the case where original and new businesses are the same, the equilibrium strategy is given in closed-form and its sensitivities to safety loadings are shown by numerical examples. At last, by comparing with the case where acquiring new business is prohibited, we show that allowing writing new policies indeed improves the performance of the insurer's risk management.</p>

scholarly journals Time-Consistent Strategies for Multi-Period Portfolio Optimization with/without the Risk-Free Asset

2018 ◽  
Vol 2018 ◽  
pp. 1-20 ◽  
Author(s):  
Zhongbao Zhou ◽  
Xianghui Liu ◽  
Helu Xiao ◽  
TianTian Ren ◽  
Wenbin Liu
Keyword(s):  
Empirical Studies ◽  
Lagrange Function ◽  
Investment Strategy ◽  
Open Loop ◽  
Investment Strategies ◽  
Variance Model ◽  
Risky Assets ◽  
Consistent Solution ◽  
Mean Variance Portfolio ◽  
Mean Variance

The pre-commitment and time-consistent strategies are the two most representative investment strategies for the classic multi-period mean-variance portfolio selection problem. In this paper, we revisit the case in which there exists one risk-free asset in the market and prove that the time-consistent solution is equivalent to the optimal open-loop solution for the classic multi-period mean-variance model. Then, we further derive the explicit time-consistent solution for the classic multi-period mean-variance model only with risky assets, by constructing a novel Lagrange function and using backward induction. Also, we prove that the Sharpe ratio with both risky and risk-free assets strictly dominates that of only with risky assets under the time-consistent strategy setting. After the theoretical investigation, we perform extensive numerical simulations and out-of-sample tests to compare the performance of pre-commitment and time-consistent strategies. The empirical studies shed light on the important question: what is the primary motivation of using the time-consistent investment strategy.

THE IMPACT OF SAVINGS WITHDRAWALS ON A BANKER’S CAPITAL HOLDINGS SUBJECT TO BASEL III ACCORD

2020 ◽  
Vol 15 (02) ◽  
pp. 2050006
Author(s):  
RYLE S. PERERA ◽  
KIMITOSHI SATO
Keyword(s):  
Stock Returns ◽  
Optimal Investment ◽  
Investment Strategy ◽  
Short Selling ◽  
Terminal Condition ◽  
Capital Regulation ◽  
Basel Iii ◽  
Investment Strategies ◽  
The Impact ◽  
Mean Variance

In this paper, we analyze the impact of savings withdrawals on a bank’s capital holdings under Basel III capital regulation. We examine the interplay between savings withdrawals and the investment strategies of a bank, by extending the classical mean–variance paradigm to investigate the bankers optimal investment strategy. We solve this via an optimization problem under a mean–variance paradigm, subject to a quadratic optimization function which incorporates a running penalization cost alongside the terminal condition. By solving the Hamilton–Jacobi–Bellman (HJB) equation, we derive the closed-form expressions for the value function as well as the banker’s optimal investment strategies. Our study provides a novel insight into the way banks allocate their capital holdings by showing that in the presence of savings withdrawals, banks will increase their risk-free asset holdings to hedge against the forthcoming deposit withdrawals whilst facing short-selling constraints. Moreover, we show that if the savings depositors of the bank are more stock-active, an economic expansion will imply a greater reduction in bank savings. As a result, the banker will reduce his/her loan portfolio and will depend on high stock returns with short-selling constraints to conform to Basel III capital regulation.

scholarly journals Equilibrium Investment Strategy for DC Pension Plan with Inflation and Stochastic Income under Heston’s SV Model

2016 ◽  
Vol 2016 ◽  
pp. 1-18 ◽  
Author(s):  
Jingyun Sun ◽  
Zhongfei Li ◽  
Yongwu Li
Keyword(s):  
Pension Plan ◽  
Investment Strategy ◽  
Investment Strategies ◽  
Value Functions ◽  
Defined Contribution ◽  
Hjb Equations ◽  
Plan Member ◽  
The Mean ◽  
Hamilton Jacobi Bellman ◽  
Mean Variance

We consider a portfolio selection problem for a defined contribution (DC) pension plan under the mean-variance criteria. We take into account the inflation risk and assume that the salary income process of the pension plan member is stochastic. Furthermore, the financial market consists of a risk-free asset, an inflation-linked bond, and a risky asset with Heston’s stochastic volatility (SV). Under the framework of game theory, we derive two extended Hamilton-Jacobi-Bellman (HJB) equations systems and give the corresponding verification theorems in both the periods of accumulation and distribution of the DC pension plan. The explicit expressions of the equilibrium investment strategies, corresponding equilibrium value functions, and the efficient frontiers are also obtained. Finally, some numerical simulations and sensitivity analysis are presented to verify our theoretical results.

scholarly journals Dynamic surplus optimization with performance- and index-linked liabilities

2021 ◽  
Author(s):  
Sascha Desmettre ◽  
Markus Wahl ◽  
Rudi Zagst
Keyword(s):  
Optimal Investment ◽  
Investment Strategy ◽  
Insurance Companies ◽  
Investment Strategies ◽  
Insurance Company ◽  
Expected Return ◽  
Close Link ◽  
Closed Form Solutions ◽  
Risky Investment ◽  
The Impact

AbstractThe increasing importance of liability-driven investment strategies and the shift towards retirement products with lower guarantees and more performance participation provide challenges for the development of portfolio optimization frameworks which cover these aspects. To this end, we establish a general and flexible terminal surplus optimization framework in continuous time, allowing for dynamic investment strategies and stochastic liabilities, which can be linked to the performance of an index or the asset portfolio of the insurance company. Besides optimality results in a fairly general surplus optimization setting, we obtain closed-form solutions for the optimal investment strategy for various specific liability models, which include the cases of index-linked and performance-linked liabilities and liabilities which are completely or only partially hedgeable. We compare the results in numerical examples and study the impact of the performance participation, unhedgeable risk components, different ways of modeling the liabilities and the relative risk aversion parameter. We find that performance- or index-linked liabilities, which provide a close link between the wealth of the insurance company and its liabilities, allow for a higher allocation in the risky investment. On the other hand, unhedgeable risks reduce the allocation in the risky investment. We conclude that, aiming at a high expected return for the policy holder, insurance companies should try to connect the performance of insurance products closely to the wealth and minimize unhedgeable risks.

OPTIMAL CONSTANT-REBALANCED PORTFOLIO INVESTMENT STRATEGIES FOR DYNAMIC PORTFOLIO SELECTION

2006 ◽  
Vol 09 (06) ◽  
pp. 951-966 ◽  
Author(s):  
ZHONG-FEI LI ◽  
KAI W. NG ◽  
KEN SENG TAN ◽  
HAILIANG YANG
Keyword(s):  
Risk Measure ◽  
Efficient Frontier ◽  
Investment Strategy ◽  
Investment Strategies ◽  
Variance Model ◽  
Optimal Constant ◽  
Black Scholes ◽  
Dynamic Portfolio ◽  
Portfolio Optimization Problem ◽  
Mean Variance

In this paper we propose a variant of the continuous-time Markowitz mean-variance model by incorporating the Earnings-at-Risk measure in the portfolio optimization problem. Under the Black-Scholes framework, we obtain closed-form expressions for the optimal constant-rebalanced portfolio (CRP) investment strategy. We also derive explicitly the corresponding mean-EaR efficient portfolio frontier, which is a generalization of the Markowitz mean-variance efficient frontier.

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