Diffusion approximations for randomly arriving expert opinions in a financial market with Gaussian drift

Sharing a resource with randomly arriving foragers.

We consider a problem of foraging where identical foragers, or predators, arrive as a stochastic Poisson process on the same patch of resource. We provide effective formulas for the expected resource intake of any of the agents, as a function of its rank, given their common functional response. We give a general theory, both in finite and infinite horizon, and show two examples of applications ...

A Gaussian Model of Expert Opinions for Supporting Design Decisions

Sequential auctions with randomly arriving buyers

We analyze a dynamic market in which buyers compete in a sequence of auctions for common value or differentiated goods. New buyers and objects may arrive at random times. Since objects are imperfect substitutes, buyers’ private values are not persistent. Instead, buyers receive new signals or draw new values in each period. We consider the use of second-price auctions for selling these objects....

On Dynamic Games with Randomly Arriving Players

We consider a dynamic game where additional players (assumed identical, even if there will be a mild departure from that hypothesis) join the game randomly according to a Bernoulli process. The problem solved here is that of computing their expected payoff as a function of time and the number of players present when they arrive, if the strategies are given. We consider both a finite horizon gam...

Drift Approximations in a Forward-Rate-Based LIBOR Market Model

In a market model of forward interest rates, a specification of the volatility structure of the forward rates uniquely determines their instantaneous drifts via the no-arbitrage condition. The resulting drifts are state-dependent and are sufficiently complicated that an explicit solution to the forward rate stochastic differential equations cannot be obtained. The lack of an analytic solution c...