scholarly journals Optimal Investment Policy for Insurers under the Constant Elasticity of Variance Model with a Correlated Random Risk Process

2020 ◽  
Vol 2020 ◽  
pp. 1-10
Author(s):  
Xiaotao Liu ◽  
Hailong Liu
Keyword(s):  
Portfolio Choice ◽  
Optimal Investment ◽  
Risk Process ◽  
Cev Model ◽  
Constant Elasticity ◽  
Economic Implications ◽  
Constant Elasticity Of Variance ◽  
Surplus Process ◽  
Hamilton Jacobi Bellman ◽  
Negative Exponential

This paper investigates the optimal portfolio choice problem for a large insurer with negative exponential utility over terminal wealth under the constant elasticity of variance (CEV) model. The surplus process is assumed to follow a diffusion approximation model with the Brownian motion in which is correlated with that driving the price of the risky asset. We first derive the corresponding Hamilton–Jacobi–Bellman (HJB) equation and then obtain explicit solutions to the value function as well as the optimal control by applying a variable change technique and the Feynman–Kac formula. Finally, we discuss the economic implications of the optimal policy.

Invariant approach to optimal investment-consumption problem: the constant elasticity of variance (CEV) model

2016 ◽  
Vol 40 (5) ◽  
pp. 1382-1395 ◽  
Author(s):  
Ahmet Bakkaloglu ◽  
Taha Aziz ◽  
Aeeman Fatima ◽  
F.M. Mahomed ◽  
Chaudry Masood Khalique
Keyword(s):  
Optimal Investment ◽  
Cev Model ◽  
Constant Elasticity ◽  
Constant Elasticity Of Variance ◽  
Invariant Approach

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.

scholarly journals Optimal Investment and Consumption Decisions under the Constant Elasticity of Variance Model

2013 ◽  
Vol 2013 ◽  
pp. 1-11 ◽  
Author(s):  
Hao Chang ◽  
Xi-min Rong ◽  
Hui Zhao ◽  
Chu-bing Zhang
Keyword(s):  
Stock Price ◽  
Optimal Investment ◽  
Dynamic Programming Principle ◽  
Power Utility ◽  
Cev Model ◽  
Constant Elasticity ◽  
Constant Elasticity Of Variance ◽  
Consumption Decisions ◽  
Optimal Investment And Consumption ◽  
Consumption Strategies

We consider an investment and consumption problem under the constant elasticity of variance (CEV) model, which is an extension of the original Merton’s problem. In the proposed model, stock price dynamics is assumed to follow a CEV model and our goal is to maximize the expected discounted utility of consumption and terminal wealth. Firstly, we apply dynamic programming principle to obtain the Hamilton-Jacobi-Bellman (HJB) equation for the value function. Secondly, we choose power utility and logarithm utility for our analysis and apply variable change technique to obtain the closed-form solutions to the optimal investment and consumption strategies. Finally, we provide a numerical example to illustrate the effect of market parameters on the optimal investment and consumption strategies.

scholarly journals Optimization Problems of Excess-of-Loss Reinsurance and Investment under the CEV Model

2013 ◽  
Vol 2013 ◽  
pp. 1-10 ◽  
Author(s):  
Qicai Li ◽  
Mengdi Gu
Keyword(s):  
Optimization Problem ◽  
Value Function ◽  
Optimization Problems ◽  
Risk Process ◽  
Model Risk ◽  
Cev Model ◽  
Constant Elasticity ◽  
Constant Elasticity Of Variance ◽  
Terminal Wealth ◽  
Better Than

We consider that the insurer purchases excess-of-loss reinsurance and invests its wealth in the constant elasticity of variance (CEV) stock market. We model risk process by Brownian motion with drift and study the optimization problem of maximizing the exponential utility of terminal wealth under the controls of excess-of-loss reinsurance and investment. Using stochastic control theory and power transformation technique, we obtain explicit expressions for the optimal polices and value function. We also show that the optimal excess-of-loss reinsurance is always better than optimal proportional reinsurance. Some numerical examples are given.

CONSTANT ELASTICITY OF VARIANCE OPTION PRICING MODEL WITH TIME-DEPENDENT PARAMETERS

2000 ◽  
Vol 03 (04) ◽  
pp. 661-674 ◽  
Author(s):  
C. F. LO ◽  
P. H. YUEN ◽  
C. H. HUI
Keyword(s):  
Option Pricing ◽  
Algebraic Approach ◽  
Time Dependent ◽  
Model Parameters ◽  
Cev Model ◽  
Constant Elasticity ◽  
Constant Elasticity Of Variance ◽  
Pricing Options ◽  
Term Structures ◽  
Option Values

This paper provides a method for pricing options in the constant elasticity of variance (CEV) model environment using the Lie-algebraic technique when the model parameters are time-dependent. Analytical solutions for the option values incorporating time-dependent model parameters are obtained in various CEV processes with different elasticity factors. The numerical results indicate that option values are sensitive to volatility term structures. It is also possible to generate further results using various functional forms for interest rate and dividend term structures. Furthermore, the Lie-algebraic approach is very simple and can be easily extended to other option pricing models with well-defined algebraic structures.

scholarly journals SHORT MATURITY ASIAN OPTIONS FOR THE CEV MODEL

2018 ◽  
Vol 33 (2) ◽  
pp. 258-290 ◽  
Author(s):  
Dan Pirjol ◽  
Lingjiong Zhu
Keyword(s):  
Analytical Approximation ◽  
Time Averaging ◽  
Asian Options ◽  
Option Prices ◽  
Asymptotic Results ◽  
Cev Model ◽  
Constant Elasticity ◽  
Constant Elasticity Of Variance ◽  
Practical Applications ◽  
Rigorous Study

We present a rigorous study of the short maturity asymptotics for Asian options with continuous-time averaging, under the assumption that the underlying asset follows the constant elasticity of variance (CEV) model. The leading order short maturity limit of the Asian option prices under the CEV model is obtained in closed form. We propose an analytical approximation for the Asian options prices which reproduces the exact short maturity asymptotics, and demonstrate good numerical agreement of the asymptotic results with Monte Carlo simulations and benchmark test cases for option parameters relevant for practical applications.

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