The productive sector of the economy, represented by a single firm employing labour to produce the consumption good, is studied in a stochastic continuous time model on a finite time interval. The firm must choose the optimal level of employment and capital investment in order to maximize its expected total profits. In this stochastic control problem the firm’s capacity is modelled as an Itô pr...

We present a new approach for the pricing of interest rate derivatives which allows a direct computation of option premiums without deriving a (BlackScholes type) partial differential equation and without explicitly solving the stochastic process for the underlying variable. The approach is tested by rederiving the prices of a zero bond and a zero bond option for a short rate environment which ...

This paper consider the Cauchy problem for Schr$ {\rm \ddot{o}} $dinger equation coupled with stochastic Benjamin-Ono equation. A priori estimates integral and nonlinear terms corresponding to coupling system are achieved by using Fourier transform restriction method introduced Bourgain. It is shown that locally well-posed as initial data in appropriate Sobolev spaces.

In this paper, to solve a linear one-dimensional Volterra  integral equation of the second kind. For this purpose using the equation form, we have defined a linear transformation and by using it's conjugate and reproducing kernel functions, we obtain a basis for the functions space.Then we obtain the solution of  integral equation in terms of the basis functions. The examples presented in this ...

We consider an optimal control problem for a Hilbert space valued linear stochastic evolution equation with additive noise and a quadratic goal function in integral form. We solve an innnite dimensional linear stochastic regulator problem by applying an augmented Lagrangian algorithm. Because of high amounts of computation time required by numerical solution of such problems we investigate a pa...

Consider a stochastic process Xn, n = 0, 1, 2, ...such that EXn → x∞ as n → ∞. The sequence {Xn} may be a deterministic one, obtained by using a numerical integration scheme, or obtained from Monte-Carlo methods involving an approximation to an integral, or a Newton-Raphson iteration to approximate the root of an equation but we will assume that we can sample from the distribution of X1, X2, .....

We introduce a class of numerical methods for highly oscillatory systems of stochastic differential equations with general noncommutative noise. We prove global weak error bounds of order two uniformly with respect to the stiffness of the oscillations, which permits to use large time steps. The approach is based on the micro-macro framework of multi-revolution composition methods recently intro...

We provide a condition for f -ergodicity of strong Markov processes at a subgeometric rate. This condition is couched in terms of a supermartingale property for a functional of the Markov process. Equivalent formulations in terms of a drift inequality on the extended generator and on the resolvent kernel are given. Results related to (f, r)-regularity and to moderate deviation principle for int...

In this paper we discuss the basket options valuation for a jump-diffusion model. The underlying asset prices follow some correlated local volatility diffusion processes with systematic jumps. We derive a forward partial integral differential equation (PIDE) for general stochastic processes and use the asymptotic expansion method to approximate the conditional expectation of the stochastic vari...