tba

With few exceptions, optimal stopping assumes that the underlying system is stopped immediately after the decision is made. 
In fact, most stoppings take time. This has been variously referred to as "time-to-build", "investment lag" and "gestation period", 
which is often non negligible. 
In this talk, we consider a class of optimal stopping/switching problems with delivery lags, or equivalently, delayed information, 
by using reflected BSDE method. As an example, we study American put option with delayed exercise, and show that it can be decomposed 
as a European put option and a premium, the latter of which involves a new optimal stopping problem where the investor decides when to stop
to collect the Greek theta of such a European option. We also give a complete characterization of the optimal exercise boundary by resorting to free boundary analysis.  

Joint work with Zhou Yang and Mihail Zervos. 

The large majority of risk-sharing transactions involve few agents, each of whom can heavily influence the structure and the prices of securities. This paper proposes a game where agents' strategic sets consist of all possible sharing securities and pricing kernels that are consistent with Arrow-Debreu sharing rules. First, it is shown that agents' best response problems have unique solutions, even when the underlying probability space is infinite. The risk-sharing Nash equilibrium admits a finite-dimensional characterisation and it is proved to exist for general number of agents and be unique in the two-agent game. In equilibrium, agents choose to declare beliefs on future random outcomes different from their actual probability assessments, and the risk-sharing securities are endogenously bounded, implying (amongst other things) loss of efficiency. In addition, an analysis regarding extremely risk tolerant agents indicates that they profit more from the Nash risk-sharing equilibrium as compared to the Arrow-Debreu one.
(Joint work with Michail Anthropelos)

Motivated by the European sovereign debt crisis, we propose a hybrid sovereign default model which combines an accessible part which takes into account the movement of the sovereign solvency and the impact of critical political events, and a totally inaccessible part for the idiosyncratic credit risk. We obtain closed-form formulas for the probability that the default occurs at political critical dates in a Markovian CEV process setting. Moreover, we introduce a generalized density framework for the hybrid default times and deduce the compensator process of default. Finally we apply the hybrid model and the generalized density to the valuation of sovereign bond and explain the significant jumps in the long-term government bond yield during the sovereign crisis.

We give necessary and sufficient conditions for the variance of the partial sums of stationary processes to be regularly varying in terms of the spectral measure associated with the shift operator. In the case of reversible Markov chains, or with normal transition operator we also give necessary and sufficient conditions in terms of the spectral measure of the transition operator.  

The two spectral measures are then linked through the use of harmonic measure.



This is joint work with S. Utev(University of Leicester, UK) and M. Peligrad (University of Cincinnati, USA).

This talk will discuss work-in-progress on the numerical approximation
of reflected diffusions arising from applications in engineering, finance
and network queueing models.  Standard numerical treatments with
uniform timesteps lead to 1/2 order strong convergence, and hence
sub-optimal behaviour when using multilevel Monte Carlo (MLMC).

In simple applications, the MLMC variance can be improved by through
a reflection "trick".  In more general multi-dimensional applications with
oblique reflections an alternative method uses adaptive timesteps, with
smaller timesteps when near the boundary.  In both cases, numerical
results indicate that we obtain the optimal MLMC complexity.

This is based on joint research with Eike Muller, Rob Scheichl and Tony
Shardlow (Bath) and Kavita Ramanan (Brown).

When estimated volatilities are not in perfect agreement with reality, delta hedged option portfolios will incur a non-zero profit-and-loss over time. There is, however, a surprisingly simple formula for the resulting hedge error, which has been known since the late 90s. We call this The Fundamental Theorem of Derivative Trading. This is a survey with twists of that result. We prove a more general version and discuss various extensions (including jumps) and applications (including deriving the Dupire-Gyo ̈ngy-Derman-Kani formula). We also consider its practical consequences both in simulation experiments and on empirical data thus demonstrating the benefits of hedging with implied volatility.

We examine the Foreign Exchange (FX) spot price spreads with and without Last Look on the transaction. We assume that brokers are risk-neutral and they quote spreads so that losses to latency arbitrageurs (LAs) are recovered from other traders in the FX market. These losses are reduced if the broker can reject, ex-post, loss-making trades by enforcing the Last Look option which is a feature of some trading venues in FX markets. For a given rejection threshold the risk-neutral broker quotes a spread to the market so that her expected profits are zero. When there is only one venue, we find that the Last Look option reduces quoted spreads. If there are two venues we show that the market reaches an equilibrium where traders have no incentive to migrate. The equilibrium can be reached with both venues coexisting, or with only one venue surviving. Moreover, when one venue enforces Last Look and the other one does not, counterintuitively, it may be the case that the Last Look venue quotes larger spreads.


a working version of the paper may be found here

http://papers.ssrn.com/sol3/papers.cfm?abstract_id=2630662