Stochastic Control and Optimal Stopping in Finance (Toulouse 12/2011)

Last updated: 09/12/2011

This is a brief real-time report on the conference OSIF (Toulouse 1, 08-09/Dec/2011)

About 40+ participants. Some are my students :-) Lunchs and coffees  are served at the conference free of charge for the participants :-). The organizers are A. Blanchet & S. Villeneuve (my colleagues at Toulouse 1)

Thursday:

9h30: Goran Peskir, Optimal detection of a hidden target

(Missed the talk due to teaching)

Prof. Peskir is the director of the MSc Programme  in Finacial Math at Manchester Univ

http://www.maths.manchester.ac.uk/~goran/

11h: Michael Ludkovski (Santa Barbara), Price discrepancies and optimal timing to buy options

– Incomplete markets

– Many compatible martingale measures, many models –> many prices

– Own model vs market price

– Optimize difference between model price and market price. The function to optimize here is the max expected value of difference with stopping time ? (Doesn’t say when to sell in his work; only optimizes the buying point of “undervalued” options when the option gets “most undervalued”).

– Example: models with defaultable stocks

– Buying options under stochastic volatility ?

– Risk-averse buyers ? Merton utility function ?

(the guy talks too fasts, runs his slides too fast)

Website of Ludkosvki: http://www.pstat.ucsb.edu/faculty/ludkovski/

http://www.pstat.ucsb.edu/faculty/ludkovski/papers.html

http://arxiv.org/abs/1008.3650 (reference for the talk)

14h: Erik Ekstrom (researcher at Uppsala Univ), Optimal timing for an asset sale under incomplete information

http://www2.math.uu.se/~ekstrom/publikation.html

Interesting toy model for momentum trading

Assumes that the drift is radom, but if > average drift then will go back to average drift in a linear way. Detect momentum to decide when to buy/sell. Stop (sell) when some probability threshold is reached.

15h30: Bruno Bouchard (Paris),  Robust non-linear pricing and stochastic target problems in game form.

http://www.ceremade.dauphine.fr/~bouchard/bouchard.htm

– Loss control (want to be sure that loss or expected value of loss doesn’t exceed certain amount)

– Write the problem in game form, with adverse controls (players who play – against you)

– Set of acceptable initial conditions (for the control to exist) ?

– G-expectation / backward stochastic diff. eq.

(Bruno has 2 students named Vu Thanh Nam and  Dang Ngoc Minh, who finished their PhD thesis this year. Both guys are OK, according to Bruno. Minh is implicated in MSc program at JVN Institute in Saigon)

– The model is general (may be too much so), allows for unknown volatility, frictions, illiquidity, etc. The notations are too complicated

– Martingale representations /submartingale (existence of Doob-Mayer decomposition for the problem ?)

– Dynamic progamming ?

– Arrives at some PDEs via variationa / duality principles / Isaacs equation ? (equilibrium –> Inf Sup = 0 –> PDE)

16h30: Romuald Elie, Exact replication under portfolio constraint a viability approach

Friday

9h: Damien Lamberton,Properties of American puts in in exponential Lévy models

Models with jumps, different from Black-Scholes

Rate of convergence for the free frontier ?

Compound Poisson case ? Case with finite variation ?

(Missed this talk due to teaching, but asked Damien for a 5-minute private lecture)

10h30: Savas Dayanik (Turkey), Optimal stopping for asset managers

Model:

– manager pays investor a rate above risk-free rate

– manager earns some %

– can decide to liquidate portfoli, pay the intestor at contracted rate, and keep the rest

-not responsible for short-all (if losses occur –> investors take the loss)

– automatic liquidation if falls below some threshold (partial protection for investors)

Question: best time to liquidate the portfolio  to maximize manager’s earnings ? How to price such products ?

11h30: Peter Tankov (Paris 7) Asymptotically optimal discretization of heding strategis with jumps.

Fukazawa’s approach (2009?) without jumps (gives better approximation than equal-time discretization)

Blumenthal-Getoor index ?

Optimization of discretization w.r.t. a cost function. (transaction costs)

Reduces the problem to a problem of discritization of a stochastic integral.

14h00: David Hobson (Warwick),  Inverse optimal stopping

Advert: Program on Fin Math in Warwick 2012. In particular, conference on optimal stopping, 16-20/July/2012

Diract stopping: models of underlying assets -> optimal stopping times -> prices of various contingent claims (e.g. American puts)

Inverse problem: given prices of various (derivative) assets, find compatible underlying models ? Models here are in temrs of diffusion or jump processes with reflections at 0 etc

15h30: Ronnie Sircar (Princeton), Energy markets as differential games

http://www.princeton.edu/~sircar/

– Games with asymmetric costs (different firms have different costs of energy production)

– Dynamic games (firms enter/exit the market when prices go up/down)

– Oil has scarcity value which increases as it runs out

– Alternative (renewable) technologies with higher costs: wind, solar, …

– Dynamic Cournot model for energy prices: price inversely linear w.r.t. production (?! why linear ? Choke price = 1 is max possible price, which corresponds to zero production (supply) )

– Nash equilibrium ?

– Value functions and feedback strategies / Hamilton-Jacobi-Bell function ?

– Blockading points: oil monopoly (plenty of oil) -> duopoly (1 alternative tech.) -> many technologies …

– Lambert-W function

– Modified version of Hotelling’s rule (1931) for exhaustible resources: marginal value funcion grows exponentially.

– Exploration and random discoveries of oil (multiple discoveries in the 80s keep prices stable; 30 discoveries in 2009 alone)

– 2-player game: oil & solar, axis game HJB system -> calculate Nash equilibrium

-Guéant-Lasry-Lions (2010) mean field games version

(Models look a bit too simplified: cost of oil is zero, cost of solar is constant …)

16h30: Mihail Zervos, (London School of Economics) Optimal stopping of 1-dim diffusions with generalized drifts.

– Skew Brownian motion models ?

– cites Peskir & Shiryaev (2006)

– mentions technical analysis (!)

Slides with very small letters, impossible to read

(didn’t follow his lecture, read resonance stuff instead)

END

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