Financial Mathematics Seminar, Spring 2006

Wed 2:30 - 3:29 pm, 106 LOV


Jan 18:

Organizational Meeting


Jan 25:

Yevgeny Goncharov, FSU -- Computing Endogenous Mortgage Rates with Randomized Quasi-Monte Carlo Simulations

In this talk we lay out the theoretical background for the problem.
Feb 1:

Manan Shah/Giray Okten, FSU -- Computing Endogenous Mortgage Rates with Randomized Quasi-Monte Carlo Simulations (Implementation)

This is the continuation of the talk started on Jan 25. This time we will discuss the implementation  of RQMC as applied to the computation of the endogenous mortgage rate process.

Feb 7 (note special day, Tue 2pm, LOV 102):

Thamayanthi Chellathurai, Canadian Imperial Bank of Commerce -- Dynamic Portfolio Selection with Nonlinear Transaction Costs

In continuous time framework, the dynamic portfolio selection problem with bankruptcy and nonlinear transaction costs is studied. The objective is to find the stochastic controls (amounts invested in the risky and risk-free assets) that maximize the expected value of the discounted utility ofterminal wealth. The problem is formulated as a non-singular stochastic optimal control problem in the sense that the necessary condition for optimality leads to explicit relation between the controls and the value function. When the transaction cost functions are piecewise linear, the characteristic curves along which the value function is constant in the transaction regions, are also piecewise linear. The no transaction region, in the presence of nonlinear transaction costs, is not a cone.


Feb 14 (note special day, Tue 2pm, LOV 102):

Kyounghee Kim, Indiana -- Morton's choice for the forward rate volatility

We will discuss "log-normal" type forward rate processes. Using the risk neutral measure, we can show that the volatility of forward rate f(t,T) has a factor f(t,T). We discuss the Morton's choice, the interest rate explosion problem and the new model with a hypothetical forward measure.
Feb 16 (note special day, Thu 2pm, LOV 102):

Traian Pirvu, British Columbia -- Maximizing Portfolio Growth Rate under Risk Constraints

This work studies the problem of optimal investment subject to risk constraints: Value-at-Risk, Tail Value-at-Risk and Limited Expected Loss. We get closed-form solutions for this problem, and find that the optimal policy is a projection of the optimal portfolio of an unconstrained log agent (the Merton proportion) onto the constraint set, with respect to the inner product induced by the variance-covariance volatilities matrix of the risky assets. In the more complicated situation of constraint sets depending on the current wealth level, we maximize the growth rate of portfolio subject to these risk constraints. We extend the analysis to a market with random coefficients, which is not necessarily complete. We also perform a robust control analysis. We find that a trader subject to Value-at-Risk and Tail Value-at-Risk is allowed to incur some risk. A trader faced with the Limited Expected Loss constraint behaves more conservatively and does not exhibit the above behavior. This is a joint work with Steven Shreve and Gordan Zitkovic.
Feb 22:

Manan Shah, FSU -- Computing Endogenous Mortgage Rates with Randomized Quasi-Monte Carlo Simulations (Implementation)

This is the continuation of the talk started on Jan 25. This time we will discuss the implementation  of RQMC as applied to the computation of the endogenous mortgage rate process.

Mar 15:

Giray Okten, FSU -- Monte Carlo for American Options I


Mar 22:

Giray Okten, FSU -- Monte Carlo for American Options II


Apr 5:

Emmanuel Salta, FSU -- Importance Sampling for Option Pricing


Apr 12: 

 Alec Kercheval, FSU -- Total risk for a portfolio of portfolios