We investigate the optimal investment problem when the interest rate is stochastic and the investor must pay proportional transaction costs when buying and selling the risky assets. We first consider a portfolio of bonds and transaction costs.We then add a stock to the portfolio, and analyze the...

The paper introduces a simple way of recording and manipulating general stochastic processes without explicit reference to a probability measure. In the new calculus, operations traditionally presented in a measure-specific way are instead captured by tracing the behaviour of jumps (also when no...

We prove the existence of statistical arbitrage opportunities for jump-diffusion models of stock prices when the jump-size distribution is assumed to have finite moments. We show that to obtain statistical arbitrage, the risky asset holding must go to zero in time. Existence of statistical...

In all investment decisions it is important to determine the degree of uncertainty associated with the valuation of a company. We propose an original and robust methodology to company valuation which replaces the traditional point estimate of the conventional Discounted Cash Flow (DCF) with a...

A novel dynamic asset-allocation approach is proposed where portfolios as well as portfolio strategies are updated at every decision period based on their past performance. For modeling, a general class of models is specified that combines a dynamic factor and a vector autoregressive model and...

This paper develops tools for analyzing properties of stochastic objective functions which take the form (formula). The paper analyzes the relationship between properties of the primitive functions, such as utility functions u and probability distributions F, and properties of the stochastic...

This chapter introduces the reader to definitions and key properties of stochastic processes that are important in finance. The discussion starts from the description of Brownian motion that describes the idea of a continuous random walk and proceeds to Ito processes that incorporate both trend...

We consider a tractable affine stochastic volatility model that generalizes the seminal Heston (1993) model by augmenting it with jumps in the instantaneous variance process. In this framework, we consider options written on the realized variance, and we examine the impact of the distribution of...

This paper reformulates the stochastic string model of Santa-Clara and Sornette (2001) using stochastic calculus with continuous semimartingales. We present some new results, such as: a) the dynamics of the short-term interest rate, b) the PDE that must be satisfied by the bond price, and c) an...