scholarly journals Optimal Investment Strategy under the CEV Model with Stochastic Interest Rate

2020 ◽  
Vol 2020 ◽  
pp. 1-11
Author(s):  
Yong He ◽  
Peimin Chen
Keyword(s):  
Interest Rate ◽  
Optimal Investment ◽  
Investment Strategy ◽  
Risky Asset ◽  
Stochastic Interest Rate ◽  
Model Parameters ◽  
Optimal Investment Strategy ◽  
Stochastic Interest ◽  
Cev Process ◽  
The Interest Rate

Interest rate is an important macrofactor that affects asset prices in the financial market. As the interest rate in the real market has the property of fluctuation, it might lead to a great bias in asset allocation if we only view the interest rate as a constant in portfolio management. In this paper, we mainly study an optimal investment strategy problem by employing a constant elasticity of variance (CEV) process and stochastic interest rate. The assets of investment for individuals are supposed to be composed of one risk-free asset and one risky asset. The interest rate for risk-free asset is assumed to follow the Cox–Ingersoll–Ross (CIR) process, and the price of risky asset follows the CEV process. The objective is to maximize the expected utility of terminal wealth. By applying the dual method, Legendre transformation, and asymptotic expansion approach, we successfully obtain an asymptotic solution for the optimal investment strategy under constant absolute risk aversion (CARA) utility function. In the end, some numerical examples are provided to support our theoretical results and to illustrate the effect of stochastic interest rates and some other model parameters on the optimal investment strategy.

scholarly journals Robust Time-Consistent Portfolio Selection for an Investor under CEV Model with Inflation Influence

2020 ◽  
Vol 2020 ◽  
pp. 1-14
Author(s):  
Peng Yang
Keyword(s):  
Probability Measure ◽  
Financial Market ◽  
Optimal Investment ◽  
Investment Strategy ◽  
Risky Asset ◽  
Control Technique ◽  
Model Parameters ◽  
Cev Model ◽  
Terminal Wealth ◽  
Optimal Investment Strategy

A robust time-consistent optimal investment strategy selection problem under inflation influence is investigated in this article. The investor may invest his wealth in a financial market, with the aim of increasing wealth. The financial market includes one risk-free asset, one risky asset, and one inflation-indexed bond. The price process of the risky asset is governed by a constant elasticity of variance (CEV) model. The investor is ambiguity-averse; he doubts about the model setting under the original probability measure. To dispel this concern, he seeks a set of alternative probability measures, which are absolutely continuous to the original probability measure. The objective of the investor is to seek a time-consistent strategy so as to maximize his expected terminal wealth meanwhile minimizing his variance of the terminal wealth in the worst-case scenario. By using the stochastic optimal control technique, we derive closed-form solutions for the optimal time-consistent investment strategy, the probability scenario, and the value function. Finally, the influences of model parameters on the optimal investment strategy and utility loss function are examined through numerical experiments.

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.

Growth Optimal Investment Strategy: The Impact of Reallocation Frequency and Heavy Tails

2012 ◽  
Vol 13 (2) ◽  
pp. 228-240 ◽  
Author(s):  
G. Bamberg ◽  
A. Neuhierl
Keyword(s):  
Heavy Tails ◽  
Geometric Mean ◽  
Asymptotic Optimality ◽  
Optimal Investment ◽  
Investment Strategy ◽  
Risky Asset ◽  
Optimal Investment Strategy ◽  
Optimality Properties ◽  
Heavy Tailed ◽  
The Impact

Abstract The strategy to maximize the long-term growth rate of final wealth (maximum expected log strategy, maximum geometric mean strategy, Kelly criterion) is based on probability theoretic underpinnings and has asymptotic optimality properties. This article reviews the allocation of wealth in a two-asset economy with one risky asset and a risk-free asset. It is also shown that the optimal fraction to be invested in the risky asset (i) depends on the length of the basic return period and (ii) is lower for heavy-tailed log returns than for light-tailed log returns.

scholarly journals Time-Consistent Investment and Reinsurance Strategies for Mean-Variance Insurers under Stochastic Interest Rate and Stochastic Volatility

Mathematics ◽  
2020 ◽  
Vol 8 (12) ◽  
pp. 2183
Author(s):  
Jiaqi Zhu ◽  
Shenghong Li
Keyword(s):  
Interest Rate ◽  
Stochastic Volatility ◽  
Financial Market ◽  
Equilibrium Strategy ◽  
Stochastic Interest Rate ◽  
Programming Approach ◽  
Model Parameters ◽  
Stochastic Interest ◽  
The Impact ◽  
Mean Variance

This paper studies the time-consistent optimal investment and reinsurance problem for mean-variance insurers when considering both stochastic interest rate and stochastic volatility in the financial market. The insurers are allowed to transfer insurance risk by proportional reinsurance or acquiring new business, and the jump-diffusion process models the surplus process. The financial market consists of a risk-free asset, a bond, and a stock modelled by Heston’s stochastic volatility model. Interest rate in the market is modelled by the Vasicek model. By using extended dynamic programming approach, we explicitly derive equilibrium reinsurance-investment strategies and value functions. In addition, we provide and prove a verification theorem and then prove the solution we get satisfies it. Moreover, sensitive analysis is given to show the impact of several model parameters on equilibrium strategy and the efficient frontier.

scholarly journals On a New Corporate Bond Pricing Model with Potential Credit Rating Change and Stochastic Interest Rate

2018 ◽  
Vol 11 (4) ◽  
pp. 87 ◽  
Author(s):  
Hong-Ming Yin ◽  
Jin Liang ◽  
Yuan Wu
Keyword(s):  
Interest Rate ◽  
Credit Rating ◽  
Corporate Bond ◽  
Bond Pricing ◽  
Stochastic Interest Rate ◽  
Pricing Model ◽  
New Model ◽  
Stochastic Interest ◽  
The Interest Rate ◽  
Rating Change

In this paper, we consider a new corporate bond-pricing model with credit-rating migration risks and a stochastic interest rate. In the new model, the criterion for rating change is based on a predetermined ratio of the corporation’s total asset and debt. Moreover, the rating changes are allowed to happen a finite number of times during the life-span of the bond. The volatility of a corporate bond price may have a jump when a credit rating for the bond is changed. Moreover, the volatility of the bond is also assumed to depend on the interest rate. This new model improves the previous existing bond models in which the rating change is only allowed to occur once with an interest-dependent volatility or multi-ratings with constant interest rate. By using a Feynman-Kac formula, we obtain a free boundary problem. Global existence and uniqueness are established when the interest rate follows a Vasicek’s stochastic process. Calibration of the model parameters and some numerical calculations are shown.

scholarly journals An Optimal Portfolio and Capital Management Strategy for Basel III Compliant Commercial Banks

2014 ◽  
Vol 2014 ◽  
pp. 1-11 ◽  
Author(s):  
Grant E. Muller ◽  
Peter J. Witbooi
Keyword(s):  
Optimal Investment ◽  
Investment Strategy ◽  
Capital Adequacy ◽  
Basel Iii ◽  
Bank Capital ◽  
Optimal Investment Strategy ◽  
Capital Adequacy Ratio ◽  
Asset Portfolio ◽  
The Interest Rate ◽  
Strategy Subject

We model a Basel III compliant commercial bank that operates in a financial market consisting of a treasury security, a marketable security, and a loan and we regard the interest rate in the market as being stochastic. We find the investment strategy that maximizes an expected utility of the bank’s asset portfolio at a future date. This entails obtaining formulas for the optimal amounts of bank capital invested in different assets. Based on the optimal investment strategy, we derive a model for the Capital Adequacy Ratio (CAR), which the Basel Committee on Banking Supervision (BCBS) introduced as a measure against banks’ susceptibility to failure. Furthermore, we consider the optimal investment strategy subject to a constant CAR at the minimum prescribed level. We derive a formula for the bank’s asset portfolio at constant (minimum) CAR value and present numerical simulations on different scenarios. Under the optimal investment strategy, the CAR is above the minimum prescribed level. The value of the asset portfolio is improved if the CAR is at its (constant) minimum value.

scholarly journals Optimal Investment for Insurers with the Extended CIR Interest Rate Model

2014 ◽  
Vol 2014 ◽  
pp. 1-12 ◽  
Author(s):  
Mei Choi Chiu ◽  
Hoi Ying Wong
Keyword(s):  
Interest Rate ◽  
Closed Form Solution ◽  
Critical Factor ◽  
Compound Poisson Process ◽  
Optimal Investment ◽  
Form Solution ◽  
Insurance Companies ◽  
Stochastic Interest Rate ◽  
Stochastic Interest ◽  
Jump Diffusion Model

A fundamental challenge for insurance companies (insurers) is to strike the best balance between optimal investment and risk management of paying insurance liabilities, especially in a low interest rate environment. The stochastic interest rate becomes a critical factor in this asset-liability management (ALM) problem. This paper derives the closed-form solution to the optimal investment problem for an insurer subject to the insurance liability of compound Poisson process and the stochastic interest rate following the extended CIR model. Therefore, the insurer’s wealth follows a jump-diffusion model with stochastic interest rate when she invests in stocks and bonds. Our problem involves maximizing the expected constant relative risk averse (CRRA) utility function subject to stochastic interest rate and Poisson shocks. After solving the stochastic optimal control problem with the HJB framework, we offer a verification theorem by proving the uniform integrability of a tight upper bound for the objective function.

Sign in / Sign up

Export Citation Format

Share Document