arXiv subjects

Dimbinirina Ramarimbahoaka

Publications and source records attributed to Dimbinirina Ramarimbahoaka.

4 recordsLinked to original sources

arXiv2015

Reflected Backward Stochastic Differential Equations for a Finite State Markov Chain Model and Applications to American Options

In this paper, we introduce a new kind of reflected backward stochastic differential equations (RBSDEs) driven by a martingale, in a Markov chain model, but not driven by Brownian motion, and give existence and uniqueness results for the new equations. Then we discuss American options in a finite state Markov chain model, in the presence of a stochastic discount function (SDF) and using the theory of the new RBSDEs. We show that there exists a constrained super-hedging strategy for an American option, which is unique in our framework as the solution to an RBSDE.

math.PR↗

arXiv2015

Some Properties of Reflected Backward Stochastic Differential Equations for a Finite State Markov Chain Model

In this paper, we provide an estimate for the solutions of reflected backward stochastic differential equations (RBSDEs) driven by a Markov chain, derive a continuous dependence property for their solutions with respect to the parameters of the equations, and show similar properties for solutions of backward stochastic differential equations (BSDEs). We finally establish a comparison result for the solutions of RBSDEs driven by a Markov chain.

math.PR↗

arXiv2014

Backward Stochastic Differential Equations with Continuous Coefficients in a Markov Chain Model and with Applications to European Options

In this paper we discuss backward stochastic differential equations with Markov chain noise, having continuous drivers. We obtain the existence of a solution which is possibly not unique. Moreover, we show there is a minimal solution for this kind of equation and derive the corresponding comparison result. This is applied to pricing of European options in a market with Markov chain noise.

math.PR↗

arXiv2014

Comparison and converse comparison theorems for backward stochastic differential equations with Markov chain noise

Comparison and converse comparison theorems are important parts of the research on backward stochastic differential equations. In this paper, we obtain comparison results for one dimensional backward stochastic differential equations with Markov chain noise, extending and generalizing previous work under natural and simplified hypotheses, and establish a converse comparison theorem for the same type of equation after giving the definition and properties of a type of nonlinear expectation: $f$-expectation.

math.PR↗