Yevgeny Goncharov, FSU -- Computing Endogenous Mortgage Rates with Randomized Quasi-Monte Carlo SimulationsIn this talk we lay out the theoretical background for the problem.
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.
Thamayanthi Chellathurai, Canadian Imperial Bank of Commerce -- Dynamic Portfolio Selection with Nonlinear Transaction CostsIn 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.
Kyounghee Kim, Indiana -- Morton's choice for the forward rate volatilityWe 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.
Traian Pirvu, British Columbia -- Maximizing Portfolio Growth Rate under Risk ConstraintsThis 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.
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.
Total risk for a portfolio of portfolios