arXiv subjects

Luis H. R. Alvarez

Publications and source records attributed to Luis H. R. Alvarez.

2 recordsLinked to original sources

arXiv2015

Optimal multi-dimensional stochastic harvesting with density-dependent prices

We prove a verification theorem for a class of singular control problems which model optimal harvesting with density-dependent prices or optimal dividend policy with capital-dependent utilities. The result is applied to solve explicitly some examples of such optimal harvesting/optimal dividend problems. In particular, we show that if the unit price decreases with population density, then the optimal harvesting policy may not exist in the ordinary sense, but can be expressed as a "chattering policy", i.e. the limit as $Δx$ and $Δt$ go to $0$ of taking out a sequence of small quantities of size $Δx$ within small time periods of size $Δt$.

math.OC↗

arXiv2010

A Loan Portfolio Model Subject to Random Liabilities and Systemic Jump Risk

We extend the Vasiček loan portfolio model to a setting where liabilities fluctuate randomly and asset values may be subject to systemic jump risk. We derive the probability distribution of the percentage loss of a uniform portfolio and analyze its properties. We find that the impact of liability risk is ambiguous and depends on the correlation between the continuous aggregate factor and the asset-liability ratio as well as on the default intensity. We also find that systemic jump risk has a significant impact on the upper percentiles of the loss distribution and, therefore, on both the VaR-measure as well as on the expected shortfall.

q-fin.RM↗