# Volume 06 (2002) No. 2

## Volume 06 (2002) No. 2

### Approximation on arcs and dendrites going to infinity in $\mathbb{C}^n$ (Extended version)

Paul M. Gauthier and E. S. Zeron

**Abstract:**

The Stone-Weierstrass approximation theorem is extended to certain unbounded sets in $\mathbb{C}^n$ . In particular, on arcs which are of locally finite length and are going to infinity, each continuous function can be approximated by entire functions.

### Bayesian procedures for pricing contingent claims: Prior information on volatility

Francisco Venegas-Martínez

**Abstract:**

This paper develops a Bayesian model for pricing derivative securities with prior information on volatility. Prior information is given in terms of expected values of levels and rates of precision: the inverse of volatility. We provide several approximate formulas, for valuing European call options, on the basis of asymptotic and polynomial approximations of Bessel functions.

### Existence of Nash equilibria in discounted nonzero-sum stochastic games with additive structure

Heriberto Hernández-Hernández

**Abstract:**

This work considers two-person nonzero-sum dynamic stochastic games when the state and action sets are Borel spaces, with possibly unbounded (immediate) cost functions, and discounted cost criteria. The aim is to prove, under suitable assumptions, the existence of a Nash equilibrium in stationary strategies. One of those assumptions is that the transition law and the cost functions have an additive (or separable) structure.

### Existence of Nash equilibria in some Markov games with discounted payoff

Carlos Gabriel Pacheco González

**Abstract:**

This work considers $N$-person stochastic game models with a discounted payoff criterion, under two different structures. First, we consider games with finite state and action spaces, and infinite horizon. Second, we consider games with Borel state space, compact action sets, and finite horizon. For each of these games, we give conditions that ensure the existence of a Nash equilibrium, which is a stationary strategy in the former case, and a Markovian strategy in the latter.