Survival and Growth with a Liability: Optimal Portfolio Strategies in Continuous Time

1997 ◽  
Author(s):  
Sid NMI1 Browne
Keyword(s):  
Continuous Time ◽  
Optimal Portfolio ◽  
Portfolio Strategies ◽  
Survival And Growth

scholarly journals Nonzero-Sum Stochastic Differential Portfolio Games under a Markovian Regime Switching Model

2015 ◽  
Vol 2015 ◽  
pp. 1-18 ◽  
Author(s):  
Chaoqun Ma ◽  
Hui Wu ◽  
Xiang Lin
Keyword(s):  
Markov Chain ◽  
Continuous Time ◽  
Regime Switching ◽  
Game Problem ◽  
Comparative Statics ◽  
Optimal Portfolio ◽  
Hjb Equations ◽  
Risky Assets ◽  
Portfolio Strategies ◽  
The Impact

We consider a nonzero-sum stochastic differential portfolio game problem in a continuous-time Markov regime switching environment when the price dynamics of the risky assets are governed by a Markov-modulated geometric Brownian motion (GBM). The market parameters, including the bank interest rate and the appreciation and volatility rates of the risky assets, switch over time according to a continuous-time Markov chain. We formulate the nonzero-sum stochastic differential portfolio game problem as two utility maximization problems of the sum process between two investors’ terminal wealth. We derive a pair of regime switching Hamilton-Jacobi-Bellman (HJB) equations and two systems of coupled HJB equations at different regimes. We obtain explicit optimal portfolio strategies and Feynman-Kac representations of the two value functions. Furthermore, we solve the system of coupled HJB equations explicitly in a special case where there are only two states in the Markov chain. Finally we provide comparative statics and numerical simulation analysis of optimal portfolio strategies and investigate the impact of regime switching on optimal portfolio strategies.

On the structure of multifactor optimal portfolio strategies

2018 ◽  
Vol 24 (3) ◽  
pp. 1043-1058
Author(s):  
Nikolai Dokuchaev
Keyword(s):  
Mutual Funds ◽  
Portfolio Selection ◽  
Optimal Strategies ◽  
Optimal Portfolio ◽  
Performance Criteria ◽  
Value Functions ◽  
Portfolio Strategies ◽  
Optimal Portfolio Selection ◽  
Admissible Strategies ◽  
Hamilton Jacobi Bellman

The paper studies problem of optimal portfolio selection. It is shown that, under some mild conditions, near optimal strategies for investors with different performance criteria can be constructed using a limited number of fixed processes (mutual funds), for a market with a larger number of available risky stocks. This implies dimension reduction for the optimal portfolio selection problem: all rational investors may achieve optimality using the same mutual funds plus a saving account. This result is obtained under mild restrictions for the utility functions without any assumptions on regularity of the value function. The proof is based on the method of dynamic programming applied indirectly to some convenient approximations of the original problem that ensure certain regularity of the value functions. To overcome technical difficulties, we use special time dependent and random constraints for admissible strategies such that the corresponding HJB (Hamilton–Jacobi–Bellman) equation admits “almost explicit” solutions generating near optimal admissible strategies featuring sufficient regularity and integrability.

scholarly journals The Optimal Portfolio Selection Model underg-Expectation

2014 ◽  
Vol 2014 ◽  
pp. 1-12 ◽  
Author(s):  
Li Li
Keyword(s):  
Prospect Theory ◽  
Decision Rule ◽  
Portfolio Selection ◽  
Continuous Time ◽  
Optimal Solution ◽  
Selection Model ◽  
Optimal Portfolio ◽  
Optimal Portfolio Selection ◽  
Choquet Expectation ◽  
Portfolio Selection Model

This paper solves the optimal portfolio selection model under the framework of the prospect theory proposed by Kahneman and Tversky in the 1970s with decision rule replaced by theg-expectation introduced by Peng. This model was established in the general continuous time setting and firstly adopted theg-expectation to replace Choquet expectation adopted in the work of Jin and Zhou, 2008. Using different S-shaped utility functions andg-functions to represent the investors' different uncertainty attitudes towards losses and gains makes the model not only more realistic but also more difficult to deal with. Although the models are mathematically complicated and sophisticated, the optimal solution turns out to be surprisingly simple, the payoff of a portfolio of two binary claims. Also I give the economic meaning of my model and the comparison with that one in the work of Jin and Zhou, 2008.

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