# Seminars at SMU Delhi

## Forthcoming Seminar(s)

August 20, 2018, 3:30 PM at Seminar Room 2
Speaker: Andrew Heunis, University of Waterloo
Title: Quadratic loss minimization with portfolio and intertemporal wealth constraints
Abstract of Talk
We address a problem of stochastic optimal control motivated by portfolio optimization in mathematical finance, the goal of which is to minimize the expected value of a general quadratic loss function of the wealth at close of trade when there is a specified convex constraint on the portfolio, together with a specified almost-sure lower-bound on intertemporal wealth over the trading interval. In the parlance of optimal control this problem exhibits the combination of a control constraint (namely the portfolio constraint) together with an almost-sure state constraint (namely the stipulated lower-bound on the wealth process over the trading interval). General optimal control problems with this combination of constraints are known to be quite challenging, not least because the Lagrange multipliers appropriate to such constraints are far from evident. The problem that we address has the additional property of being convex, and this is key to the application of an ingenious variational method of R.T. Rockafellar for abstract convex optimization which leads to a vector space of dual variables, together with a dual functional on the space of dual variables, such that the dual problem of maximizing the dual functional is guaranteed to have a solution (or Lagrange multiplier) when the intertemporal state constraint satisfies a simple and natural Slater condition. This yields necessary and sufficient conditions for the optimality of a candidate portfolio (i.e. control) process, as well as the construction (in principle!) of an optimal portfolio.
August 23, 2018, 3:30 PM at Seminar Room 2
Speaker: Sudeshna Basu, George Washington University
Title: Linear Hahn Banach Extension of module homomorphisms in Hilbert and Banach modules
Abstract of Talk

The notion of linear Hahn-Banach extension operator was first studied in detail by Heinrich and Mankiewicz (1982). Previously, J. Lindenstrauss (1966) studied similar versions of this notion in the context of non separable reflexive Banach spaces. Subsequently, Sims and Yost (1989) proved the existence of linear Hahn-Banach extension operators via interspersing subspaces in a purely Banach space theoretic set up. In this paper, we study similar questions in the context of Banach modules and module homomorphisms, in particular, Banach algebras of operators on Banach spaces. Based on Dales, Kania, Kochanek, Kozmider and Laustsen(2013), and also Kania and Laustsen (2017), we give complete answers for reflexive Banach spaces and the non-reflexive space constructed by Kania and Laustsen from the celebrated Argyros-Haydon's space with few operators.

This is a joint work with Ajit Iqbal singh.

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