Time reversal and last passage time of diffusions with applications to credit risk management

Finance and Stochastics - We study time reversal, last passage time and $h$ -transform of linear diffusions. For general diffusions with killing, we obtain the probability density of the last...     

Labour market discrimination and the macroeconomy

We measure the discriminatory ethnic and gender wage gaps in Georgia. Gender wage discrimination is larger than the ethnic wage discrimination. We use the estimated gaps in a general‐to‐specific vector autoregression framework to test for Granger causality between discrimination and growth, and estimate the long‐run effects of each variable on the other. Granger causality is found to be bidirectional, but it is only the net long‐run effect of discrimination on growth that is a large and highly significant negative effect. In the long‐run, a 10% increase in ethnic (gender) discrimination reduces economic growth by 3%–4% (8%–10%). Additionally, ethnic and gender wage differentials are found to be counter‐cyclical.     

A direct solution method for pricing options in regime‐switching models

Pricing financial or real options with arbitrary payoffs in regime‐switching models is an important problem in finance. Mathematically, it is to solve, under certain standard assumptions, a general form of optimal stopping problems in regime‐switching models. In this article, we reduce an optimal stopping problem with an arbitrary value function in a two‐regime environment to a pair of optimal stopping problems without regime switching. We then propose a method for finding optimal stopping rules using the techniques available for nonswitching problems. In contrast to other methods, our systematic solution procedure is more direct as we first obtain the explicit form of the value functions. In the end, we discuss an option pricing problem, which may not be dealt with by the conventional methods, demonstrating the simplicity of our approach.