In this paper, we examine an exchange economy with a financial market composed of three assets: a share of a stock, an European call option written on the stock, and a riskless bond.

We study the exponential utility indifference valuation of a contingent claim B in an incomplete market driven by two Brownian motions. The claim depends on a nontradable asset stochastically correlated with the traded asset available for hedging. We use martingale arguments to provide upper and...

This paper studies modelling and existence issues for market models of option prices in a continuous-time framework with one stock, one bond and a family of European call options for one fixed maturity and all strikes. After arguing that (classical) implied volatilities are ill-suited for...

We apply perturbation theory to solve the optimal control problem of an investor with time-additive power utility over intermediate consumption and final wealth. Under general conditions we show existence of a power series representation for the prevailing optimal consumption and investment...

We solve analytically the Merton's problem of an investor with time-additive power utility. For general state dynamics, we prove existence of two power series representations of the relevant optimal policies and value functions, which hold for all admissible risk aversion parameters. We...

Three years after the seminal work of Black and Scholes [3] on the pricing of European options,Scholes [18] presented a paper in which the impact of taxation on the value of an option is analyzed.We restart this discussion in a simple binomial setting emphasizing the economic principlesof...

The binomial model has been used to price a wide variety of equity and interest rateoptions for more than two decades. Originally developed by Cox, Ross, and Rubinsteinto clarify the basic pricing principle of its continuous-time counterpart with reduced mathematicalrequirements, the approach...

In the past decades several versions of the binomial model for option pricing, originallyintroduced by COX, ROSS, AND RUBINSTEIN, have been discussed in the financeliterature. Some of these approaches model an arbitrage-free market in the discrete setupwhereas others attain this property only in...

This paper studies modelling and existence issues for market models of stochastic implied volatility in a continuous-time framework with one stock, one bank account and a family of European options for all maturities with a fixed payoff function h. We first characterize absence of arbitrage in...

A generalized correlated random walk is a process X_k of partial sums of random variables Y_j such that (X,Y) forms a Markov chain. For a sequence X^n of such processes where each Y^n_j takes only two values, we prove weak convergence to a diffusion process whose generator is explicitly...