A diffusion {xt}, 0<= t <= 1, is considered and its semimartingale decomposition obtained when the terminal value x1 is known, in addition to the history of the diffusion up to time t.

By analogy with the theory of Backward Stochastic Differential Equations, we define Backward Stochastic Difference Equations on spaces related to discrete time, finite state processes. This paper considers these processes as constructions in their own right, not as approximations to the...

The integrand, when a martingale under an equivalent measure is represented as a stochastic integral, is determined by elementary methods in the Markov situation. Applications to hedging portfolios in finance are described.

The paper considers a diffusion evolving in n. The stochastic differential equations giving the same process, but with the time parameter evolving in the negative direction, are obtained under a certain integrability hypothesis when the diffusion has a density function on a time varying...

Hidden Markov Models provide an adaptive method of estimating random quantities, that is, they not only consider the quantity under investigation but also revise the parameters of the model. Results of a recent paper are used to determine the implicit interest rate of an asset whose value is...

The converse comparison theorem has received much attention in the theory of backward stochastic differential equations (BSDEs). However, no such theorem has been proved for anticipated BSDEs. In this paper, we derive a converse comparison theorem by first giving an existence and uniqueness...