This paper develops a general stochastic model of a frictionless security market with continuous trading. The vector price process is given by a semimartingale of a certain class, and the general stochastic integral is used to represent capital gains. Within the framework of this model, we...

A paper by the same authors in the 1981 volume of Stochastic Processes and Their Applications presented a general model, based on martingales and stochastic integrals, for the economic problem of investing in a portfolio of securities. In particular, and using the terminology developed therein,...

We consider a two-dimensional diffusion process Z(t) = [Z1(t), Z2(t)] that lives in the half strip {0 [less-than-or-equals, slant] Z1 [less-than-or-equals, slant] 1, 0 [less-than-or-equals, slant] Z2 < [infinity]}. On the interior of this state space, Z behaves like a standard Brownian motion (independent components with zero drift and unit variance), and there is instantaneous reflection at the boundary. The reflection is in a direction normal to the boundary at Z1 = 1 and Z2 = 0, but at Z1 = 0 the reflection is at an angle [theta] below the normal (0<[theta]<[theta]). This process Z is shown to arise as the diffusion limit of a certain tandem storage or queuing system. It is shown that Z(t) has a nondefective limit distribution F as t --> [infinity], and the marginal distributions of F are computed explicitly. The marginal limit...</[infinity]}.>

Consider a storage system (such as an inventory or bank account) whose content fluctuates as a Brownian Motion X = {X(t), t [greater-or-equal, slanted] 0} in the absence of any control. Let Y = {Y(t), t [greater-or-equal, slanted] 0} and Z = {Z(t), t [greater-or-equal, slanted] 0} be...

We consider a generalization of the classical model of collective risk theory. It is assumed that the cumulative income of a firm is given by a process X with stationary independent increments, and that interest is earned continuously on the firm's assets. Then Y(t), the assets of the firm at...

Finite and infinite planning horizon Markov decision problems are formulated for a class of jump processes with general state and action spaces and controls which are measurable functions on the time axis taking values in an appropriate metrizable vector space. For the finite horizon problem,...