Recently Kifer (2000) introduced the concept of an Israeli (or Game) option. That is a general American-type option with the added possibility that the writer may terminate the contract early inducing a payment exceeding the holder’s claim had they exercised at that moment. Kifer shows that...

The main purpose of the paper is to provide a mathematical background for the theory of bond markets similar to that available for stock markets. We suggest two constructions of stochastic integrals with respect to processes taking values in a space of continuous functions. Such integrals are...

Consider a model of a financial market with a stock driven by a Lévy process and constant interest rate. A closed formula for prices of perpetual American call options in terms of the overall supremum of the Lévy process, and a corresponding closed formula for perpetual American put options...

In this paper, we study the nonemptiness and the shape of the exercise region of American options written on several assets. Our contribution is threefold. First, we state an analytic theorem which characterizes the nonemptiness of the exercise region. Second, we study a particular class of...

We prove new error estimates for the Longstaff–Schwartz algorithm. We establish an <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$O(\log^{\frac{1}{2}}(N)N^{-\frac{1}{2}})$</EquationSource> </InlineEquation> convergence rate for the expected L <Superscript>2</Superscript> sample error of this algorithm (where N is the number of Monte Carlo sample paths), whenever the approximation architecture of...</superscript></equationsource></inlineequation>

In this paper we give the closed form solution of some optimal stopping problems for processes derived from a diffusion with jumps. Within the possible applications, the results can be interpreted as pricing perpetual American Options under diffusion-jump information.

The main result of the paper is a stability theorem for the Snell envelope under convergence in distribution of the underlying processes: more precisely, we prove that if a sequence $(X^n)$ of stochastic processes converges in distribution for the Skorokhod topology to a process $X$ and...

Recently, various authors proposed Monte-Carlo methods for the computation of American option prices, based on least squares regression. The purpose of this paper is to analyze an algorithm due to Longstaff and Schwartz. This algorithm involves two types of approximation. Approximation one:...