SCIENTIFIC PROGRAMS AND ACTIVITIES

THE FIELDS INSTITUTE FOR RESEARCH IN MATHEMATICAL SCIENCES
20th ANNIVERSARY YEAR

TBA

Thursday, March 14, 2013
5:00 p.m.
Stewart Library

Takashi Shibata, Tokyo Metroplitan University
Investment timing, debt structure, and financing constraints

We introduce debt issuance limit constraints along with market debt and bank debt to consider how financial frictions affect investment, financing, and debt structure strategies. Our model provides four important results. First, a firm is more likely to issue market debt than bank debt when its debt issuance limit increases. Second, investment strategies are nonmonotonic with respect to debt issuance limits. Third, debt issuance limits distort the relationship between a firm's equity value and investment strategy. Finally, debt issuance limit constraints lead to debt holders experiencing low risk and low returns. That is, the more severe the debt issuance limits, the lower the credit spreads and default probabilities. Our theoretical results are consistent with stylized facts and empirical results. This is joint work with Michi Nishihara, Osaka University.

Mikhail Zhitlukhin, University of Manchester
Disorder detection problems for diffusion processes and their applications in finance

We consider several questions related to problems of quickest disorder detection for diffusion processes. By a disorder we mean an unknown moment of time when the structure of an observable process changes, e.g. a drift appears. In the first part of the talk we present general results on the existence of Markov sufficient statistics and show how disorder detection problems can be reduced to Markovian optimal stopping problems. In particular, we solve disorder problems for Brownian motion with a disorder on a finite time segment. In the second part of the talk we apply the results obtained to practical questions of choosing the optimal time to sell an asset which initially has a positive trend and then the trend reverses at some unknown moment of time. We test our criteria on real market data and show that they give relatively good results. (This is a joint work with A.N. Shiryaev and W.T. Ziemba.)

Thursday Sept. 20
5:00 p.m.

The worldwide market of variable annuities (VAs) has been rapidly growing since their introduction in the mid-1980s in the United States. These fund-linked annuity products, which have become an essential part of the retirement plans in many countries, are often combined with additional living and death benefits. Since they are usually of a complex nature, consistent pricing of variable annuities becomes a difficult task. As there is often a trade-off between a realistic model and analytical tractability, several studies in the literature either focus on closed-form solutions, by simplifying the contract setups and the modeling assumptions, or propose numerical methods for the multi-factor models. This work aims to fill this gap by showing how the explicit representations for prices of some of the VA products can be derived in a hybrid model for insurance and market risks.

Thursday Sept. 6
5:00 p.m.

Lane Hughston (University College London)
Signal Processing with Lévy Information

Lévy processes, which have stationary independent increments, are ideal for modelling the various types of noise that can arise in communication channels. If a Lévy process admits exponential moments, then there exists a parametric family of measure changes called Esscher transformations. If the parameter is replaced with an independent random variable, the true value of which represents a “message”, then under the transformed measure the original Lévy process takes on the character of an “information process”. In this paper we develop a theory of such Lévy information processes. The underlying Lévy process, which we call the fiducial process, represents the “noise type”. Each such noise type is capable of carrying a message of a certain specification. A number of examples are worked out in detail, including information processes of the Brownian, Poisson, gamma, variance gamma, negative binomial, inverse Gaussian, and normal inverse Gaussian type. Although in general there is no additive decomposition of information into signal and noise, one is led nevertheless for each noise type to a well-defined scheme for signal detection and enhancement relevant to a variety of practical situations. In this presentation we also consider applications to the theory of finance. (Joint work with Dorje C. Brody, Brunel University, and Xun Yang, Imperial College London. The paper can be found at: arxiv.org/abs/1207.4028v1)