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...

Linear Methods are often used to compute approximate solutions to dynamic models, as these models often cannot be solved analytically. Linear methods are very popular, as they can easily be implemented. Also, they provide a useful starting point for understanding more elaborate numerical...

This paper provides a new technique for representing discrete time nonlinear dynamic stochastic time invariant maps. Using this new series representation, the paper augments the usual solution strategy with an additional set of constraints thereby enhancing algorithm reliability. The paper also...

Binary random variables often refer to such as customers that are present or not, roads that are open or not, machines that are operable or not. At the same time, stochastic programs often apply to situations where penalties are accumulated when demand is not met, travel times are too long, or...

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...

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...

In the seismological and geophysics literature, it is suggested by numerous authors that the elapsed time between two earthquakes at a given location should be represented by either an exponential or Weibull distribution. In addition, the seismic gap hypothesis states that large waiting times...

Measurement error causes a loss of distributional information, preventing the researcher from applying the deterministic revealed-preference tools at the individual level. This paper proposes a new statistical revealed-preference framework that is applicable to such cases. We use our framework...

Simulation models of economic, financial and business risk factors are widely used to assess risks and support decision-making. Extensive literature on scenario generation methods aims at describing some underlying stochastic processes with the least number of scenarios to overcome the "curse of...

In this short note, we prove by an appropriate change of variables that the SVI implied volatility parameterization presented in Gatheral's book and the large-time asymptotic of the Heston implied volatility agree algebraically, thus confirming a conjecture from Gatheral as well as providing a...