Past talks in the Seminar on Applications in Mathematics series can be found at:
http://www.math.virginia.edu/Institute/SAM.htm

2005


November 18, 2005:
Financial Valuation of Mortality Risk via the Instantaneous Sharpe Ratio (paper joint with Moshe A. Milevsky and S. David Promislow)
Virginia Young (University of Michigan)
3:00pm, KER 317

We develop a theory for pricing in an incomplete market by assuming that the writer (buyer) of a financial contract requires compensation for the unhedgeable risk in the form of a pre-specified instantaneous Sharpe ratio. We demonstrate our method by pricing a simple mortality-contingent claim; specifically, we derive the partial differential equation that the price solves. We show that the resulting price satisfies a number of desirable properties by applying comparison arguments.   [Paper in pdf]

November 17, 2005:
Minimizing the Probability of Lifetime Ruin under Borrowing Constraints
Virginia Young (University of Michigan)
4:00pm, KER 317
(Refreshments precede the talk at 3:30 in Kerchof 314)

We determine the optimal investment strategy of an individual who targets a given rate of consumption and who seeks to minimize the probability of going bankrupt before she dies, also known as lifetime ruin. We impose two types of borrowing constraints. First, we do not allow the individual to borrow money to invest in the risky asset nor to sell the risky asset short. However, the latter is not a real restriction because in the unconstrained case, the individual does not sell the risky asset short. Second, we allow the individual to borrow money but only at a rate that is higher than the rate earned on the riskless asset. We consider two forms of the consumption function: (1) The individual consumes at a constant (real) dollar rate, and (2) the individual consumes a constant proportion of her wealth. The first is arguably more realistic, but the second is closely connected with Merton's model of optimal consumption and investment under power utility. We demonstrate that connection in this paper, as well as include a numerical example to illustrate our results. [Paper in pdf]

November 7-11, 2005:
Lectures on Levy Processes, Stochastic Calculus and Financial Applications
David Applebaum (University of Sheffield)

Please see below website for additional details:
http://www.math.virginia.edu/Institute/talks_pdf.htm
October 26, 2005:
IMS presents John Allen Paulos

http://www.math.virginia.edu/paulos/paulos.htm
October 22-23, 2005
Miniconference on the Variance Gamma and Related Models in Mathematical Finance
http://conferences.math.virginia.edu/vg
October 21, 2005
Special Seminar: Shortfall Risk Measures, and Utility Maximization under Model Uncertainty
Stefan Weber (Cornell)
4:30pm, Clark Hall 101
We consider the problem of utility maximization under model uncertainty in the presence of both cost and risk constraints. Downside risk is measured by utility-based shortfall risk. We first review the properties of utility-based shortfall risk. The acceptance sets of these risk measures are defined in terms of a convex loss function and a fixed threshold level. Second, we discuss utility maximization under both cost and risk constraints, if there is no model uncertainty. By means of its dual problem, the optimization problem can explicitly be solved. Finally, we characterize the solution of the robust utility maximization problem under robust constraints. In this case, model uncertainty involves three aspects the measurement of the utility, the cost and the downside risk. We assume that investors take a worst case approach. The talk is based on joint work with Anne Gundel (Humboldt-Universität zu Berlin).
September 30, 2005
4:00-5:00pm in Physics 203
Colloquium Jointly Sponsored by the Institute of Mathematical Science, the Physics Department, and the History Department
All Was Light Isaac Newton's Revolutions
Speaker: Mordechai Feingold (CalTech)
This will be a general presentation accessible to a wide audience.
July 10-13, 2005
Workshop and Conference on Probability, Financial Derivatives, and Asset Pricing http://conferences.math.virginia.edu/finance
January 21, 2005, 3:00pm, KER 317
SAM talk: Multivariate heavy tails, asymptotic independence and beyond
Sidney Resnick (Cornell University)
A random vector having a distribution which is multivariate regularly varying at infinity can have a dependence structure which is hard to specify in practice. One extreme situation is "asymptotic independence" which roughly describes the situation where the random vector's components are not simultaneously large. Asymptotic independence makes it difficult to specify probabilities of extreme events unless one makes further assumptions. We discuss one subclass of heavy tailed asymptotically independent distributions where the joint distribution possesses hidden regular variation. We discuss detection of this phenomena along with other extensions into conditional models. Some applications to network and exchange rate data is provided.
Thursday, January 20, 2005, 4:30pm, KER 317 (Probability Seminar)
Maxima of stationary solutions for SDEs driven by fractional Brownian motion
Boris Buchmann (Australian National University, Canberra)
We propose a class of stochastic differential equations driven by fractional Brownian motion. This class contains the Langevin equation and a fractional Vasicek model. The stationary solution is constructed explicitly. Furthermore, we consider maxima of these solutions over finite time horizons and give a complete characterization of the maximum domain of attraction to the classical extreme value distributions.