OPTIMAL MULTIPLE STOPPING AND VALUATION OF SWING OPTIONS

The connection between optimal stopping of random systems and the theory of the Snell envelop is well understood, and its application to the pricing of American contingent claims is well known. Motivated by the pricing of swing contracts (whose recall components can be viewed as contingent claims with multiple exercises of American type) we investigate the mathematical generalization of these results to the case of possible multiple stopping. We prove existence of the multiple exercise policies in a fairly general set-up. We then concentrate on the Black–Scholes model for which we give a constructive solution in the perpetual case, and an approximation procedure in the finite horizon case. The last two sections of the paper are devoted to numerical results. We illustrate the theoretical results of the perpetual case, and in the finite horizon case, we introduce numerical approximation algorithms based on ideas of the Malliavin calculus.     

Pandemic effects in the Solow growth model

We show how diseases can affect economic growth in a Solow growth model, with population growth and no technical progress, but modified to include a saving rate that depends on the individual health status. We successively insert this model into the SIS (susceptible–infected–susceptible) and SIR (susceptible–infected–recovered) models of disease spreading. In these two models, the spread of the infection proceeds according to the so-called basic reproductive number. This number determines in which of the two possible equilibria, the disease-free or the pandemic equilibrium, the economy ends. We show that output per capita is always lower in the pandemic steady state, which implies a contraction in the economy's production possibilities frontier.     

The influence of economic research on financial mathematics: Evidence from the last 25 years

This is an attempt to review some of the breakthroughs in economic research as they impacted the nascent field of financial mathematics over the last 25 years. Because of the prominent role of Finance and Stochastics in the definition of this emerging field, I try to view things through the lens of its published papers, and I try to stay away from financial engineering applications.