An optimal investment strategy with maximal risk aversion and its ruin probability in the presence of stochastic volatility on investments

2013 ◽  
Vol 53 (1) ◽  
pp. 1-13 ◽  
Author(s):  
Mohamed Badaoui ◽  
Begoña Fernández
Keyword(s):  
Risk Aversion ◽  
Stochastic Volatility ◽  
Ruin Probability ◽  
Optimal Investment ◽  
Investment Strategy ◽  
Optimal Investment Strategy

An optimal investment strategy with maximal risk aversion and its ruin probability

2008 ◽  
Vol 68 (1) ◽  
pp. 159-179 ◽  
Author(s):  
Begoña Fernández ◽  
Daniel Hernández-Hernández ◽  
Ana Meda ◽  
Patricia Saavedra
Keyword(s):  
Risk Aversion ◽  
Ruin Probability ◽  
Optimal Investment ◽  
Investment Strategy ◽  
Optimal Investment Strategy

scholarly journals Perturbative Expansion of FBSDE in an Incomplete Market with Stochastic Volatility

2012 ◽  
Vol 02 (03) ◽  
pp. 1250015 ◽  
Author(s):  
Masaaki Fujii ◽  
Akihiko Takahashi
Keyword(s):  
Stochastic Volatility ◽  
Optimal Investment ◽  
Investment Strategy ◽  
Incomplete Market ◽  
Perturbative Expansion ◽  
Quadratic Growth ◽  
Third Order ◽  
Hedging Strategies ◽  
Optimal Investment Strategy ◽  
Expansion Technique

In this work, we apply our newly proposed perturbative expansion technique to a quadratic growth FBSDE appearing in an incomplete market with stochastic volatility that is not perfectly hedgeable. By combining standard asymptotic expansion technique for the underlying volatility process, we derive explicit expression for the solution of the FBSDE up to the third order of volatility-of-volatility for its level, and the fourth order for its diffusion part that can be directly translated into the optimal investment strategy. We compare our approximation with the exact solution, which is known to be derived by the Cole–Hopf transformation in this popular setup. The result is very encouraging and shows good accuracy of the approximation up to quite long maturities. Since our new methodology can be extended straightforwardly to multi-dimensional setups, we expect it will open real possibilities to obtain explicit optimal portfolios or hedging strategies under realistic assumptions.

scholarly journals Optimal Investment-Consumption Strategy under Inflation in a Markovian Regime-Switching Market

2016 ◽  
Vol 2016 ◽  
pp. 1-17 ◽  
Author(s):  
Huiling Wu
Keyword(s):  
Regime Switching ◽  
Stock Price ◽  
Optimal Investment ◽  
Investment Strategy ◽  
Power Utility ◽  
Optimal Investment Strategy ◽  
Admissible Strategies ◽  
Definition Of ◽  
Markovian Regime Switching ◽  
Optimal Investment And Consumption

This paper studies an investment-consumption problem under inflation. The consumption price level, the prices of the available assets, and the coefficient of the power utility are assumed to be sensitive to the states of underlying economy modulated by a continuous-time Markovian chain. The definition of admissible strategies and the verification theory corresponding to this stochastic control problem are presented. The analytical expression of the optimal investment strategy is derived. The existence, boundedness, and feasibility of the optimal consumption are proven. Finally, we analyze in detail by mathematical and numerical analysis how the risk aversion, the correlation coefficient between the inflation and the stock price, the inflation parameters, and the coefficient of utility affect the optimal investment and consumption strategy.

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.

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