A Sensitive Inter-Temporal Equilibrium Model For Relative Well-Being

Londoño, Jaime A.

doi:10.2139/ssrn.2580671

Cited by 1 publication

(2 citation statements)

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“…Computable solutions are not known in general settings, since hedgeability of the income structure does not necessarily allow for the optimal portfolio to be hedgeable in the standard models (see Karatzas and shreve [9, Sections 3.6 and 4.4]). However, current models of equilibrium allow for the existence of state variables that model the dynamics of the relevant variables of the economy as in Merton [10], Breeden [11], Cox et al [12], or Londoño [13] to cite just a few.…”

Section: Introductionmentioning

confidence: 99%

“…In the spirit of Merton [10], Breeden [11], and Cox et al [12] we assume a Markovian setting for the "state variables" that includes not only the price processes but also additional variables that describe the evolution of the economy. This setting proved to be the right framework to study equilibrium problems, since equilibrium defines restrictions on the variables that make them take values on manifolds; see Londoño [13].…”

Section: Introductionmentioning

confidence: 99%

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State-Dependent Utilities and Incomplete Markets

Londoño

2013

Mathematical Problems in Engineering

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The problem of optimal consumption and investment for an agent that does not influence the market is solved. The optimization criteria are based on a state-dependent utility functional as proposed in Londoño (2009). The proposed solution is given in any market without state-tame arbitrage opportunities, includes several utilities structures, and includes incomplete markets where there are multiple state variables. The solutions obtained for optimal wealths consumptions, and portfolios are explicit and easily computable; the main condition for the result to hold is that the income process of each agent is hedgeable, requiring a natural condition on employer and employee to agree on a contract whose risk can be managed by both parties. In this paper we also developed a theory of markets when the processes are generalization of Brownian flows on manifolds, since this framework shows to be the natural one whenever the problem of intertemporal equilibrium is addressed.

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