Let X1 X2 Xn be independent and identically distributed with distribution function F . A statistician may choose two X values from the sequence by means of two stopping rules t1 t2, with the goal of maximizing E Xt1 ∨ Xt2 . We describe the optimal stopping rules and the asymptotic behavior of the optimal expected stopping values, V 2 n , as n → , when F is the exponential distribution. Specific...

We describe asymptotically optimal Bayesian and frequentist solutions to the problem of sequential change-point detection in multiparameter exponential families when the pre-and post-change parameters are unknown. In this connection we also address certain issues recently raised by Mei (2008) concerning performance criteria for detection rules in this setting.

Let Xn, . . . , X1 be i.i.d. random variables with distribution function F . A statistician, knowing F , observes the X values sequentially and is given two chances to choose X’s using stopping rules. The statistician’s goal is to stop at a value of X as small as possible. Let V 2 n equal the expectation of the smaller of the two values chosen by the statistician when proceeding optimally. We o...

This paper integrates the problem of designing corporate bankruptcy rules into a theory of optimal debt structure. We show that, in an optimal contracting framework with imperfect renegotiation, having multiple creditors increases a firm’s debt capacity while increasing its incentives to default strategically. The optimal debt contract gives creditors claims that are jointly inconsistent in cas...

The present paper investigates theoretical performance of various Bayesian wavelet shrinkage rules in a nonparametric regression model with i.i.d. errors which are not necessarily normally distributed. The main purpose is comparison of various Bayesian models in terms of their frequentist asymptotic optimality in Sobolev and Besov spaces. We establish a relationship between hyperparameters, ver...

Abstract Elementary proofs of classical theorems on pricing perpetual call and put options in the standard Black-Scholes model are given. The method presented does not rely on stochastic calculus and is also applied to give prices and optimal stopping rules for perpetual call options when the stock is driven by a Lévy process with no positive jumps, and for perpetual put options for stocks driv...

This paper investigates the optimal design of diversification rules for regulated enterprises. Diversification by a regulated firm generates profit in non-core markets that can be shared with core customers. However, a diversified firm may divert its attention and effort to its non-core operations, causing consumer welfare in the core market to decline. When diversification is permitted, lower ...

It is obvious that an optimal policy should consider main dimensions of the phenomenon that can affect the transmission mechanism of that policy. In an open economy, it is expected that variables of the foreign sector play important role in its economic behavior. Therefore, it needs that any optimal policy in an open economy to design in such a way which involves changes in the foreign sector. ...