Stochastic-Volatility, Jump-Diffusion Optimal Portfolio Problem with Jumps in Returns and Volatility

2011 ◽  
Author(s):  
Floyd B. Hanson
Keyword(s):  
Stochastic Volatility ◽  
Jump Diffusion ◽  
Optimal Portfolio ◽  
Portfolio Problem

scholarly journals Portfolio problems based on jump-diffusion models

Filomat ◽  
2012 ◽  
Vol 26 (3) ◽  
pp. 573-583 ◽  
Author(s):  
Tiantian Liu ◽  
Jun Zhao ◽  
Peibiao Zhao
Keyword(s):  
Differential Equation ◽  
Stochastic Differential Equation ◽  
Asset Price ◽  
Efficient Frontier ◽  
Jump Diffusion ◽  
Natural Generalization ◽  
Optimal Portfolio ◽  
Linear Quadratic ◽  
Price Process ◽  
Portfolio Problem

Zhou and Li [49] by virtue of stochastic linear-quadratic control theory studied the optimal portfolio problems with the asset price process satisfying a diffusion stochastic differential equation, and proposed the celebrated LQ framework and the efficient frontier for the given portfolio problem. In this paper, we consider the optimal portfolio problems based on the asset price process satisfying a jump-diffusion stochastic differential equation. Similarly, we also arrive at the efficient frontier of the optimal portfolio selection problem. The conclusions obtained here can be regarded as a natural generalization of the work by Zhou and Li [49].

A NOTE ON A NEW APPROACH TO BOTH PRICE AND VOLATILITY JUMPS: AN APPLICATION TO THE PORTFOLIO MODEL

2016 ◽  
Vol 58 (2) ◽  
pp. 182-186 ◽  
Author(s):  
MOAWIA ALGHALITH
Keyword(s):  
Closed Form ◽  
Stochastic Volatility ◽  
Viscosity Solutions ◽  
Value Function ◽  
Jump Diffusion ◽  
Optimal Portfolio ◽  
New Approach ◽  
Closed Form Solutions ◽  
Volatility Function ◽  
The Value Function

A new approach to jump diffusion is introduced, where the jump is treated as a vertical shift of the price (or volatility) function. This method is simpler than the previous methods and it is applied to the portfolio model with a stochastic volatility. Moreover, closed-form solutions for the optimal portfolio are obtained. The optimal closed-form solutions are derived when the value function is not smooth, without relying on the method of viscosity solutions.

Optimal portfolio and consumption with habit formation in a jump diffusion market

2013 ◽  
Vol 222 ◽  
pp. 391-401 ◽  
Author(s):  
Xinfeng Ruan ◽  
Wenli Zhu ◽  
Jin Hu ◽  
Jiexiang Huang
Keyword(s):  
Habit Formation ◽  
Jump Diffusion ◽  
Optimal Portfolio
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