DIVIDEND OPTIMIZATION FOR A REGIME-SWITCHING DIFFUSION MODEL WITH RESTRICTED DIVIDEND RATES

2014 ◽  
Vol 44 (2) ◽  
pp. 459-494 ◽  
Author(s):  
Jinxia Zhu
Keyword(s):  
Markov Chain ◽  
Regime Switching ◽  
Critical Level ◽  
Sufficient Conditions ◽  
Insurance Company ◽  
Threshold Strategy ◽  
Regime Switching Model ◽  
Switching Model ◽  
Switching Diffusion ◽  
Optimal Dividend

AbstractWe consider the optimal dividend control problem to find an optimal strategy under the constraint that dividend rates is restricted such that the expected total discounted dividends are maximized for an insurance company. The evolution of the reserve is modeled by a diffusion process with drift and volatility coefficients modulated by an observable Markov chain. We consider the regime-switching threshold strategy which pays out dividends at the maximal possible rate when the current reserve is above some critical level dependent on the regime of the Markov chain at the time, and pays nothing when the reserve is below that level. We give sufficient conditions under which such type of strategy is optimal for the regime-switching model.

scholarly journals A CONDITIONAL MARKOV REGIME SWITCHING MODEL TO STUDY MARGINS: APPLICATION TO THE FRENCH FUEL RETAIL MARKETS

2015 ◽  
Vol 21 (2) ◽  
Author(s):  
RAPHAËL HOMAYOUN BOROUMAND ◽  
STÉPHANE GOUTTE ◽  
SIMON PORCHER ◽  
THOMAS PORCHER
Keyword(s):  
Markov Chain ◽  
Market Structure ◽  
Regime Switching ◽  
Markov Regime Switching ◽  
Regime Switching Model ◽  
Switching Model ◽  
The Standard Model ◽  
High Volatility ◽  
Volatility Regimes ◽  
Markov Regime Switching Model

<p class="ESRBODY">This paper uses a regime-switching model that is built on mean-reverting and local volatility processes combined with two Markov regime-switching processes to understand the market structure of the French fuel retail market over the period 1990-2013. The volatility structure of these models depends on a first exogenous Markov chain, whereas the drift structure depends on a conditional Markov chain with respect to the first one. Our model allows us to identify mean reverting and switches in the volatility regimes of the margins. In the standard model of cartel coordination, volatility can increase competition. We find that cartelization is even stronger in phases of high volatility. Our best explanation is that consumers consider volatility in prices to be a change in market structure and are therefore less likely to search for lower-priced retailers, thus increasing the market power of the oligopoly. Our findings provide a better understanding of the behavior of oligopolies.</p>

scholarly journals Option pricing in a regime-switching model using the fast Fourier transform

2006 ◽  
Vol 2006 ◽  
pp. 1-22 ◽  
Author(s):  
R. H. Liu ◽  
Q. Zhang ◽  
G. Yin
Keyword(s):  
Fourier Transform ◽  
Markov Chain ◽  
Fast Fourier Transform ◽  
Regime Switching ◽  
Asset Price ◽  
Sample Path ◽  
Regime Switching Model ◽  
Switching Model ◽  
Large State Space ◽  
Black Scholes

This paper is concerned with fast Fourier transform (FFT) approach to option valuation, where the underlying asset price is governed by a regime-switching geometric Brownian motion. An FFT method for the regime-switching model is developed first. Aiming at reducing computational complexity, a near-optimal FFT scheme is proposed when the modulating Markov chain has a large state space. To test the FFT method, a novel semi-Monte Carlo simulation algorithm is developed. This method takes advantage of the observation that the option value for a given sample path of the underlying Markov chain can be calculated using the Black-Scholes formula. Finally, numerical results are reported.

scholarly journals Weak convergence of stochastic integrals with respect to the state occupation measure of a Markov chain

2021 ◽  
Vol 58 (2) ◽  
pp. 372-393
Author(s):  
H. M. Jansen
Keyword(s):  
Markov Chain ◽  
Weak Convergence ◽  
Regime Switching ◽  
Sufficient Conditions ◽  
The State ◽  
Stochastic Integrals ◽  
Occupation Measure ◽  
Generator Matrix ◽  
Markov Modulated ◽  
Erlang Loss

AbstractOur aim is to find sufficient conditions for weak convergence of stochastic integrals with respect to the state occupation measure of a Markov chain. First, we study properties of the state indicator function and the state occupation measure of a Markov chain. In particular, we establish weak convergence of the state occupation measure under a scaling of the generator matrix. Then, relying on the connection between the state occupation measure and the Dynkin martingale, we provide sufficient conditions for weak convergence of stochastic integrals with respect to the state occupation measure. We apply our results to derive diffusion limits for the Markov-modulated Erlang loss model and the regime-switching Cox–Ingersoll–Ross process.

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