Math Finance Colloquium Schedule
The MF Colloquiums are held regularly on Mondays, 2:15-3:15, at KAP 414.
Fall 2010
Spring 2010
Fall 2009
Spring 2009
| Date | Speaker | Affiliation | Title of talk | Comment |
|---|---|---|---|---|
| 9/3/10 |
T. I. Lai | Stanford University | Sequential Monte Carlo methods for rare event simulation |
Friday, 3:30-4:30 |
| 9/13/10 | Zhen Wu | Shandong University, China | BSDEs with Markov Chains and Application to Homogenization of PDEs System | |
| 9/24/10 |
20th Anniversary Celebration of CAMS |
Friday, 2:30-4:30 |
||
| 10/11/10 | Mihai Sirbu | UT Austin |
Optimal investment with high-watermark performance fee | |
| 10/22/10 | Michael Magill |
USC | Reforming Capitalism | Friday, 3:30-4:30 |
| 10/29/10 | Steven Kou | Columbia University | Pricing Asian Options under a General Jump Diffusion Model | Friday, 3:30-4:30 |
| 11/8/10 | Marco Fritelli |
University of Milano, UCSB | On Quasiconvex Dynamic Risk Measures | |
| 11/15/10 |
Olaf Menkens | Dublin City University, Ireland | Optimising Proportional Reinsurance Using a Worst Case Scenario Approach | |
| 11/16/10 |
Morgan Stanley Recruiting Event | TBA | Tuesday, 12:00-4:30 |
|
| 12/6/10 | Shaolin Ji | Shandong University, China and Boston U. |
TBA |
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FRIDAY, 9/03/10, KAP 414, 3:30 - 4:30 PM
T. L. Lai (Stanford University)
"Sequential Monte Carlo methods for rare event simulation"
We introduce a Monte Carlo method that involves sequential importance sampling and resampling (SISR) to compute probabilities of rare events in complex stochastic systems. As an illustration of the method, we consider its application to the computation of credit portfolio loss distributions and demonstrate its advantages over recent advances in this mathematical finance topic by using importance sampling (IS) and interacting particle systems (IPS). We develop a martingale representation for SISR, which we use to derive the standard error of the SISR estimator and show how the importance measure and resampling scheme can be chosen to achieve asymptotic efficiency. Applications to large deviation probabilities of light-tailed and heavy-tailed random walks and their Markovian extensions are also considered.
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MONDAY, 9/13/10, KAP 414, 2:15-3:15 PM
Zhen Wu (Shandong University, China)
"BSDEs with Markov Chains and Application to Homogenization of PDEs System"
In this talk, we consider one kind of backward stochastic differential equations (BSDEs in short) where the coefficient f is affected by a Markovian switching. We obtain the existence and uniqueness results for the solution to this kind of BSDEs. And then we give the weak convergence result of BSDEs with a singular-perturbed Markov chain which is involved in a large state space. At last, as an application of theoretical results, we show the homogenization of one system of partial differential equations (PDEs in short).
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MONDAY, 10/11/10, KAP 414, 2:15-3:15 PM
Mihai Sirbu (University of Texas, Austin)
"Optimal investment with high-watermark performance fee"
We consider the problem of optimal investment and consumption when the
investment opportunity is represented by a hedge-fund charging proportional
fees on profit. The value of the fund evolves as a geometric Brownian motion
and the performance of the investment and consumption strategy is measured
using discounted power utility from consumption on infinite horizon. The resulting
stochastic control problem is solved using dynamic programming arguments.
We show by analytical methods that the associated Hamilton-Jacobi-Bellman equation
has a smooth solution, and then obtain the existence and representation of the optimal
control in feedback form using verification arguments. The presentation is based on
joint work with Karel Janecek.
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FRIDAY, 10/22/10, KAP 414, 3:30 - 4:30 PM
Michael Magill (University of Southern California)
"Reforming Capitalism"
that applying the state of nature approach to describing uncertainty for corporations
(the standard approach of finance) can be shown to be inappropriate, indeed largely
meaningless. Instead we should adopt a more realistic statistical approach i.e. think of
the outcome of production as a random variable described by its probability distribution
over the possible outputs (at date 1) where the distribution is influenced by the investment
made by the firm at date 0. This apparently innocent change has a major impact on what the
firm should do, since its investment decision now has an external effect on its employees and
consumers. The paper shows in the simplest setting how stochastic general equilibrium theory
with production has to be altered when we replace the standard Arrow-Debreu approach by this
probability approach. It shows that we are led to a major revision of the theory of corporate governance,
the standard theory of operating a corporation in the best interest of its shareholder by maximizing
its profit, is replaced by a stakeholder theory of the corporation in which the firm must also take into
account the interests of its workers and consumers.
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FRIDAY, 10/29/10, KAP 414, 3:30 - 4:30 PM
Steven Kou (Columbia University)
"Pricing Asian Options under a General Jump Diffusion Model"
We obtain a closed-form solution for the double-Laplace transform of Asian options under the hyper-exponential jump diffusion model (HEM). Similar results are only available previously in the special case of Black-Scholes model (BSM). Even in the case of BSM, our approach is simpler as we essentially use only the Ito's formula and do not need more advanced results such as those of Bessel processes and Lamperti's representation. Furthermore, our approach is more general as it applies to the HEM. As a by-product we also show that a well-known recursion relating to Asian options has a unique solution in a probabilistic sense. The double-Laplace transforms can be inverted numerically via a two-sided Euler inversion algorithm. Numerical results indicate that our pricing method is fast, stable, and accurate.
This is a joint work with Ning Cai, Hong Kong Univ. of Science and Technology.
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MONDAY, 11/8/10, KAP 414, 2:15-3:15 PM
Marco Frittelli (University of Milano, Italy and USCB)
"On Quasiconvex Dynamic Risk Measures"
We introduce Quasiconvex Dynamic Risk Measures and study their dual representation under different continuity assumptions. We provide the financial motivation for this analysis, its decision theory foundation
and its link with the notion of Acceptability Indices.
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MONDAY, 11/15/10, KAP 414, 2:15-3:15 PM
Olaf Menkens (University of Dublin, Ireland)
"Optimising Proportional Reinsurance Using a Worst Case Scenario Approach"
This presentation considers the problem of an insurance company to optimise its reserve process by proportional reinsurance. Usually, the reinsurance level will be determined by a ruin probability constraint or by minimising the ruin probability (see e.g. Hipp and Vogt (2003), Schmidli (2001, 2002, and 2004), or Eisenberg and Schmidli (2008)). Instead of conditioning on the ruin probability, this presentation will maximise the controlled reserve process by a worst--case scenario approach.
The worst--case scenario approach has been introduced in the context of portfolio optimisation by Korn and Wilmott (2002). This approach has been extended so far in various ways (e.g. considering different utility function (Korn and Menkens (2005)), optimising investment portfolio of an insurance company (Korn (2005)), in a stochastic differential game context (Korn and Steffensen (2007)).
We start by making the so--called small claims assumption, that is the claims will be modelled as a Brownian motion with drift. Second, the claims will be modelled as the sum of a Brownian motion with drift and a Poisson process and third, claims will be modelled as a Poisson process. Results will be computed, analysed, and compared with the results of minimising the ruin probability.
This is work in progress and joint research with Ralf Korn (TU Kaiserslautern) and Mogens Steffensen (U of Copenhagen).
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