This paper is concerned with the compound Poisson risk model and two generalized models with still Poisson claim arrivals. One extension incorporates inhomogeneity in the premium input and in the claim arrival process, while the other takes into account possible dependence between the successive...

In economics the main efficiency criterion is that of Pareto-optimality. For problems of distributing a social endowment a central notion of fairness is no-envy (each agent should receive a bundle at least as good, according to her own preferences, as any of the other agent's bundle). For most...

Direct construction of the probability distribution function for a Poisson binomial random variable, where success probabilities may vary from trial to trial, requires on the order of <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$$2^{n}$$</EquationSource> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink"> <msup> <mn>2</mn> <mi>n</mi> </msup> </math> </EquationSource> </InlineEquation> calculations, and is computationally infeasible for all but modest sized problems. An...</equationsource></equationsource></inlineequation>

For the problem of adjudicating conflicting claims, we study lower bounds on the awards of each agent. We propose extending a lower bound by performing the following operation: (i) for each problem, assign the lower bound and revise the problem accordingly; (ii) assign the bound of the revised...

Dynamic models with inequality constraints pose a challenging problem for two major reasons: Dynamic Programming techniques often necessitate a non established differentiability of the value function, while Euler equation based techniques have problematic or unknown convergence properties. This...

This paper deals with an insurance portfolio that covers two interdependent risks. The central model is a discrete-time bivariate risk process with independent claim increments. A continuous-time version of compound Poisson type is also examined. Our main purpose is to develop a numerical method...

We study a decentralized trading model as in Peters (1984a), where heterogeneous market participants face a trade-off between price and trade probability. We present a novel proof of existence of a unique demand vector in Nash equilibrium, based on a recursive approach that exploits the...

In this paper, a multi-dimensional risk model with common shocks is studied. Using a simple probabilistic approach via observing the risk processes at claim instants, recursive integral formulas are developed for the survival probabilities as well as for a class of Gerber–Shiu expected...

We obtain a recursive formulation for a general class of contracting problems involving incentive constraints. These constraints make the corresponding maximization sup problems non-recursive. Our approach consists of studying a recursive Lagrangian. Under standard general conditions, there is a...