Hypoelliptic diffusion processes can be used to model a variety of phenomena in applications ranging from molecular dynamics to audio signal analysis. We study parameter estimation for such processes in situations where we observe some components of the solution at discrete times. Since exact...

We consider models for the valuation of derivative securities that depend on foreign exchange rates. We derive partial differential equations for option prices in an arbitrage-free market with stochastic volatility. By use of standard techniques, and under the assumption of fast mean reversion...

A basket default swap (BDS) is a credit derivative with contingent payments that are triggered by a combination of default events of the reference entities. A forward-starting basket default swap (FBDS) is a BDS starting at a specified future time. Existing analytic or semi-analytic methods for...

In this paper, we consider the following inverse problem for the first hitting time distribution: given a Wiener process with a random initial state, probability distribution, F(t), and a linear boundary, b(t)=[mu]t, find a distribution of the initial state such that the distribution of the...

Diversity is a key issue in the provision of critical publicly provided goods such as clean drinking water and education. To develop institutions that address this issue, it is critical that we understand the mechanisms through which diversity and public goods are related. A simple model of...

Social capital appears to have significant consequences for economic development, yet we know little about how social capital develops or the role of government institutions in promoting or hindering that development. The two key approaches to social capital, as civic engagement or as...

By facilitating mutually beneficial transactions, trust is a crucial ingredient for economic development. We explore the determinants of trust by studying a model in which agents rely on imperfectly enforceable contracts to support cooperation in a prisoners’ dilemma production game. We show...

The latest generation of volatility derivatives goes beyond variance and volatility swaps and probe our ability to price realized variance and sojourn times along bridges for the underlying stock price process. In this paper, we give an operator algebraic treatment of this problem based on Dyson...