Stochastic Analysis and Stochastic Finance Seminar

Optimal Order Execution

Speaker(s): 
Jose Infante Acevedo(Ecole de Pons)
Date: 
Thursday, November 8, 2012 - 5:00pm
Location: 
Rudower Chaussee 25, Room 1.115

Splitting and cubature schemes for stochastic partial differential equations

Speaker(s): 
Philipp Drörsek(ETH Zürich)
Date: 
Thursday, November 8, 2012 - 4:00pm
Location: 
Rudower Chaussee 25, Room 1.115

Optimal liquidation with log-linear price impact and transaction costs

Speaker(s): 
Mihail Zervos (London School of Economics)
Date: 
Thursday, October 25, 2012 - 5:00pm
Location: 
Rudower Chaussee 25, Room 1.115

Monotonicity of the CDO term structure models

Speaker(s): 
Michal Barski (Universität Leipzig)
Date: 
Thursday, October 25, 2012 - 4:00pm
Location: 
Rudower Chaussee 25, Room 1.115

Good Deals: a new perspective

Speaker(s): 
Hirbod Assa (Concordia University)
Date: 
Thursday, July 5, 2012 - 5:00pm
Location: 
TU Berlin, MA041 Strasse des 17. Juni 136, 10623 Berlin

We study Good Deals in a scenario whereby a representative agent uses decision-making tools based on a risk measure, and where the market prices are given by a sub-linear pricing rule. We consider a hedging problem where the shortfall risk is minimized subject to a given budget constraint. First, we observe that, given a coherent risk measure, the existence of a Good Deal is equivalent to the incompatibility between the pricing rule and the risk measure.

Finite-time pricing kernel models

Speaker(s): 
Andrea Macrina (King's College London)
Date: 
Wednesday, July 4, 2012 - 4:00pm
Location: 
TU Berlin, MA041 Strasse des 17. Juni 136, 10623 Berlin

Finite-time pricing kernel models are proposed, which (a) are driven by Markov processes, (b) produce positive interest rate processes, and (c) can be automatically calibrated to the term structure of bond prices. For a specific class of pricing models, it is possible to obtain closed-form expressions for the interest rate dynamics and the market price of risk. Likewise, analytical formulae may be obtained simultaneously for bonds and interest rate derivatives, such as interest rate caplets and swaptions.

Utility maximization in a binomial model with proportional transaction costs

Speaker(s): 
Christian Bayer (WIAS)
Date: 
Thursday, June 21, 2012 - 5:00pm
Location: 
TU Berlin, MA041 Strasse des 17. Juni 136, 10623 Berlin

We study the classical problem of maximizing the expected utility of the terminal value of a portfolio in a binomial (Cox-Ross-Rubinstein) model. By classical results [Merton 1969] both in discrete and continuous time, the optimal portfolio strategy in a friction-less market is is given by keeping the proportion between the wealth invested in the stock and the total portfolio wealth constant.

C^{1,1} regularity for degenerate elliptic obstacle problems in mathematical finance

Speaker(s): 
Paul Feehan (Rutgers University)
Date: 
Thursday, June 21, 2012 - 4:00pm
Location: 
TU Berlin, MA041 Strasse des 17. Juni 136, 10623 Berlin

The Heston stochastic volatility process is a degenerate diffusion process where the degeneracy in the diffusion coefficient is proportional to the square root of the distance to the boundary of the half-plane. The generator of this process with killing, called the elliptic Heston operator, is a second-order, degenerate-elliptic partial differential operator, where the degeneracy in the operator symbol is proportional to the distance to the boundary of the half-plane.

Optimal posting distance of limit orders: a stochastic algorithm approach

Speaker(s): 
Sophie Laruelle (Paris)
Date: 
Thursday, June 7, 2012 - 5:00pm
Location: 
TU Berlin, MA041 Strasse des 17. Juni 136, 10623 Berlin

Considering that a trader or a trading algorithm interacting with markets during continuous auctions can be modelled by an iterating procedure adjusting the price at which he posts orders at a given rhythm, this paper proposes a procedure minimizing his costs. We prove the $a.s.$ convergence of the algorithm under assumptions on the cost function and give some practical criteria on model parameters to ensure that the conditions to use the algorithm are fulfilled (using notably principle of opposite monotony).

A flexible matrix Libor model with smiles

Speaker(s): 
Alessandro Gnoatto (LMU München)
Date: 
Thursday, June 7, 2012 - 4:00pm
Location: 
TU Berlin, MA041, Strasse des 17. Juni 136, 10623 Berlin

We present a flexible approach for the valuation of interest rate derivatives based on Affine Processes. We extend the methodology proposed in Keller-Ressel et al. (2009) by changing the choice of the state space. We provide semi-closed-form solutions for the pricing of caps and floors. We then show that it is possible to price swaptions in a multifactor setting with a good degree of analytical tractability. This is done via the Edgeworth expansion approach developed in Collin-Dufresne and Goldstein (2002).

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