35 research outputs found
Optimal life insurance purchase, consumption and investment on a financial market with multi-dimensional diffusive terms
We introduce an extension to Merton’s famous continuous time model of optimal
consumption and investment, in the spirit of previous works by Pliska and Ye, to allow for
a wage earner to have a random lifetime and to use a portion of the income to purchase life
insurance in order to provide for his estate, while investing his savings in a financial market
comprised of one risk-free security and an arbitrary number of risky securities driven by multidimensional
Brownian motion. We then provide a detailed analysis of the optimal consumption,
investment, and insurance purchase strategies for the wage earner whose goal is to maximize
the expected utility obtained from his family consumption, from the size of the estate in the
event of premature death, and from the size of the estate at the time of retirement. We use
dynamic programming methods to obtain explicit solutions for the case of discounted constant
relative risk aversion utility functions and describe new analytical results which are presented
together with the corresponding economic interpretations.We thank the Calouste Gulbenkian Foundation, PRODYN-ESF, POCTI and POSI by FCT and Ministerio da Ciencia, Tecnologia e Ensino Superior, CEMAPRE, LIAAD-INESC Porto LA, Centro de Matematica da Universidade do Minho and Centro de Matematica da Universidade do Porto for their financial support. D. Pinheiro's research was supported by FCT - Fundacao para a Ciencia e Tecnologia program 'Ciencia 2007' and project 'Randomness in Deterministic Dynamical Systems and Applications' (PTDC/MAT/105448/2008). I. Duarte's research was supported by FCT - Fundacao para a Ciencia e Tecnologia grant with reference SFRH/BD/33502/2008
Eroding market stability by proliferation of financial instruments
We contrast Arbitrage Pricing Theory (APT), the theoretical basis for the
development of financial instruments, with a dynamical picture of an
interacting market, in a simple setting. The proliferation of financial
instruments apparently provides more means for risk diversification, making the
market more efficient and complete. In the simple market of interacting traders
discussed here, the proliferation of financial instruments erodes systemic
stability and it drives the market to a critical state characterized by large
susceptibility, strong fluctuations and enhanced correlations among risks. This
suggests that the hypothesis of APT may not be compatible with a stable market
dynamics. In this perspective, market stability acquires the properties of a
common good, which suggests that appropriate measures should be introduced in
derivative markets, to preserve stability.Comment: 26 pages, 8 figure
Heat release by controlled continuous-time Markov jump processes
We derive the equations governing the protocols minimizing the heat released
by a continuous-time Markov jump process on a one-dimensional countable state
space during a transition between assigned initial and final probability
distributions in a finite time horizon. In particular, we identify the
hypotheses on the transition rates under which the optimal control strategy and
the probability distribution of the Markov jump problem obey a system of
differential equations of Hamilton-Bellman-Jacobi-type. As the state-space mesh
tends to zero, these equations converge to those satisfied by the diffusion
process minimizing the heat released in the Langevin formulation of the same
problem. We also show that in full analogy with the continuum case, heat
minimization is equivalent to entropy production minimization. Thus, our
results may be interpreted as a refined version of the second law of
thermodynamics.Comment: final version, section 2.1 revised, 26 pages, 3 figure
Dynamic versus one-period completeness in event-tree security markets
Event-tree security markets, Dynamic completeness, One-period completeness, Law of one price, G10, G12,