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**Contingent claims valuation when the security price is a combination of an Itō process and a random point process.**
*(English)*
Zbl 0645.90009

This paper develops several results in the modern theory of contingent claims valuation in a frictionless security market with continuous trading. The price model is a semi-martingale with a certain structure, making the return of the security a sum of an Itō process and a random, marked point process. Dynamic equilibrium prices are known to be of this form in an Arrow-Debreu economy, so that there is no real limitation in our approach. This class of models is also advantageous from an applied point of view.

Within this framework we investigate how the model behaves under the equivalent martingale measure in the \(P^*\)-equilibrium economy, where discounted security prices are marginales. Here we present some new results showing how the marked point process affects prices of contingent claims in equilibrium.

We derive a new class of

single server on a network, relaxing the assumption that the server is always available for service, and explicitly accounting for queueing. The resulting queueing-location model allows for an arbitrary number of priority classes. Properties of the objective function are developed and algorithms presented for obtaining the optimal location on tree and cyclic networks. Sensitivity analysis with respect to the average arrival rate of calls is investigated. A numerical example is presented to illustrate the results of this paper. The major conclusions of the paper include: (a) the optimal location need not be at a node of the network, (b) the optimal location changes as a function of the arrival rate of calls into the system, (c) the optimal location is usually different from that obtained by grouping all calls into one priority class.

Within this framework we investigate how the model behaves under the equivalent martingale measure in the \(P^*\)-equilibrium economy, where discounted security prices are marginales. Here we present some new results showing how the marked point process affects prices of contingent claims in equilibrium.

We derive a new class of

single server on a network, relaxing the assumption that the server is always available for service, and explicitly accounting for queueing. The resulting queueing-location model allows for an arbitrary number of priority classes. Properties of the objective function are developed and algorithms presented for obtaining the optimal location on tree and cyclic networks. Sensitivity analysis with respect to the average arrival rate of calls is investigated. A numerical example is presented to illustrate the results of this paper. The major conclusions of the paper include: (a) the optimal location need not be at a node of the network, (b) the optimal location changes as a function of the arrival rate of calls into the system, (c) the optimal location is usually different from that obtained by grouping all calls into one priority class.

Reviewer: R.Beedgen

### Keywords:

financial economics; contingent claims valuation; frictionless security market; continuous trading; semi-martingale; queueing-location model; priority classes; tree; cyclic networks; sensitivity analysis
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\textit{K. K. Aase}, Stochastic Processes Appl. 28, No. 2, 185--220 (1988; Zbl 0645.90009)

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