scholarly journals Minimal Expected Time in Drawdown through Investment for an Insurance Diffusion Model

Risks ◽  
2021 ◽  
Vol 9 (1) ◽  
pp. 17
Author(s):  
Leonie Violetta Brinker
Keyword(s):  
Brownian Motion ◽  
Optimal Investment ◽  
Investment Strategy ◽  
Insurance Company ◽  
Piecewise Monotone ◽  
Expected Time ◽  
Optimal Investment Strategy ◽  
Running Maximum ◽  
Hamilton Jacobi Bellman ◽  
The Value Function

Consider an insurance company whose surplus is modelled by an arithmetic Brownian motion of not necessarily positive drift. Additionally, the insurer has the possibility to invest in a stock modelled by a geometric Brownian motion independent of the surplus. Our key variable is the (absolute) drawdown Δ of the surplus X, defined as the distance to its running maximum X¯. Large, long-lasting drawdowns are unfavourable for the insurance company. We consider the stochastic optimisation problem of minimising the expected time that the drawdown is larger than a positive critical value (weighted by a discounting factor) under investment. A fixed-point argument is used to show that the value function is the unique solution to the Hamilton–Jacobi–Bellman equation related to the problem. It turns out that the optimal investment strategy is given by a piecewise monotone and continuously differentiable function of the current drawdown. Several numerical examples illustrate our findings.

scholarly journals Optimal Investment and Proportional Reinsurance in a Regime-Switching Market Model under Forward Preferences

Mathematics ◽  
2021 ◽  
Vol 9 (14) ◽  
pp. 1610
Author(s):  
Katia Colaneri ◽  
Alessandra Cretarola ◽  
Benedetta Salterini
Keyword(s):  
Stock Prices ◽  
Regime Switching ◽  
Common Factor ◽  
Optimal Investment ◽  
Investment Strategy ◽  
Market Model ◽  
Sensitivity Analyses ◽  
Model Parameters ◽  
Insurance Company ◽  
Optimal Investment Strategy

In this paper, we study the optimal investment and reinsurance problem of an insurance company whose investment preferences are described via a forward dynamic exponential utility in a regime-switching market model. Financial and actuarial frameworks are dependent since stock prices and insurance claims vary according to a common factor given by a continuous time finite state Markov chain. We construct the value function and we prove that it is a forward dynamic utility. Then, we characterize the optimal investment strategy and the optimal proportional level of reinsurance. We also perform numerical experiments and provide sensitivity analyses with respect to some model parameters.

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.

scholarly journals Optimal Investment Strategy for Risky Assets

1998 ◽  
Vol 01 (03) ◽  
pp. 377-387 ◽  
Author(s):  
Sergei Maslov ◽  
Yi-Cheng Zhang
Keyword(s):  
Growth Rate ◽  
Brownian Motion ◽  
Continuous Time ◽  
Optimal Strategy ◽  
Optimal Investment ◽  
Investment Strategy ◽  
Risky Assets ◽  
Average Return ◽  
Optimal Investment Strategy

We design an optimal strategy for investment in a portfolio of assets subject to a multiplicative Brownian motion. The strategy provides the maximal typical long-term growth rate of investor's capital. We determine the optimal fraction of capital that an investor should keep in risky assets as well as weights of different assets in an optimal portfolio. In this approach both average return and volatility of an asset are relevant indicators determining its optimal weight. Our results are particularly relevant for very risky assets when traditional continuous-time Gaussian portfolio theories are no longer applicable.

scholarly journals The Role of Inflation-indexed Bond in Optimal Management of Defined Contribution Pension Plan During the Decumulation Phrase

2018 ◽  
Author(s):  
Xiaoyi Zhang ◽  
Junyi Guo
Keyword(s):  
Pension Plan ◽  
Optimal Investment ◽  
Investment Strategy ◽  
Programming Approach ◽  
Defined Contribution ◽  
Inflation Risk ◽  
Dynamic Programming Approach ◽  
Optimal Investment Strategy ◽  
Defined Contribution Pension Plan ◽  
Hamilton Jacobi Bellman

In this paper we investigate the optimal investment strategy for a defined contribution (DC) pension plan during the decumulation phrase which is risk-averse and pays close attention to inflation risk. The plan aims to maximize the expected constant relative risk aversion (CRRA) utility from the terminal wealth by investing the wealth in a financial market consisting of an inflation-indexed bond, an ordinary zero coupon bond and a risk-free asset. We derive the optimal investment strategy in closed-form using the dynamic programming approach by solving the corresponding Hamilton-Jacobi-Bellman (HJB) equation. Our theoretical and numerical results reveal that under some rational assumptions, an inflation-indexed bond do has significant advantage to hedge inflation risk.

scholarly journals Precommitted Investment Strategy versus Time-Consistent Investment Strategy for a Dual Risk Model

2014 ◽  
Vol 2014 ◽  
pp. 1-13 ◽  
Author(s):  
Lidong Zhang ◽  
Ximin Rong ◽  
Ziping Du
Keyword(s):  
Risk Model ◽  
Optimal Investment ◽  
Investment Strategy ◽  
Bellman Equations ◽  
Optimal Investment Strategy ◽  
Optimization Principle ◽  
Dual Risk Model ◽  
Strategy Versus ◽  
Hamilton Jacobi Bellman ◽  
Original Time

We are concerned with optimal investment strategy for a dual risk model. We assume that the company can invest into a risk-free asset and a risky asset. Short-selling and borrowing money are allowed. Due to lack of iterated-expectation property, the Bellman Optimization Principle does not hold. Thus we investigate the precommitted strategy and time-consistent strategy, respectively. We take three steps to derive the precommitted investment strategy. Furthermore, the time-consistent investment strategy is also obtained by solving the extended Hamilton-Jacobi-Bellman equations. We compare the precommitted strategy with time-consistent strategy and find that these different strategies have different advantages: the former can make value function maximized at the original timet=0and the latter strategy is time-consistent for the whole time horizon. Finally, numerical analysis is presented for our results.

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 TheCEVModel and Its Application in a Study of Optimal Investment Strategy

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Aiyin Wang ◽  
Ls Yong ◽  
Yang Wang ◽  
Xuanjun Luo
Keyword(s):  
Optimal Investment ◽  
Investment Strategy ◽  
Legendre Transform ◽  
Investment Strategies ◽  
Approximation Solution ◽  
Constant Elasticity ◽  
Constant Elasticity Of Variance ◽  
Optimal Investment Strategy ◽  
Hamilton Jacobi Bellman ◽  
Exponential Utility Function

The constant elasticity of variance (CEV) model is used to describe the price of the risky asset. Maximizing the expected utility relating to the Hamilton-Jacobi-Bellman (HJB) equation which describes the optimal investment strategies, we obtain a partial differential equation. Applying the Legendre transform, we transform the equation into a dual problem and obtain an approximation solution and an optimal investment strategies for the exponential utility function.

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