Title

Itô-Wentzell for measure dependent random fields under full and conditional measure flows

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Abstract

We show several Itô-Wentzell formulae on Wiener spaces for real-valued maps depending on measures. We present both the full measure-flow and the marginal-flow cases where the measure flow derivatives are understood in the sense of Lions.

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This talk has been cancelled.

Title

A Case Study on Pareto Optimality for Collaborative Stochastic Games

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Abstract

Pareto Optimality (PO) is an important concept in game theory to measure global efficiency when players collaborate. In this talk, we start with the PO for a class of continuous-time stochastic games when the number of players is finite. The derivation of PO strategies is based on the formulation and analysis of an auxiliary N-dimensional central controller’s stochastic control problem, including its regularity property of the value function and the existence of the solution to the associated Skorokhod problem. This PO strategy is then compared with the set of (non-unique) NEs strategies under the notion of Price of Anarchy (PoA). The upper bond of PoA is derived explicitly in terms of model parameters. Finally, we characterize analytically the precise difference between the PO and the associated McKean-Vlasov control problem with an infinite number of players, in terms of the covariance structure between the optimally controlled dynamics of players and characteristics of the no-action region for the game. This is based on joint work with Xin Guo (UC Berkeley).

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Title

Boundary renormalisation of stochastic PDEs
 

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Abstract

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We discuss solution theories of singular SPDEs endowed with various boundary conditions. In several examples  nontrivial boundary effects arise and another layer of renormalisation is required. We outline how these are connected to spatial singularities of simple trees in equations like the KPZ, PAM, of Phi^4.

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Title

When does portfolio compression reduce systemic risk?

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Abstract

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We analyse the consequences of portfolio compression on systemic risk. Portfolio compression is a post-trading netting mechanism that reduces gross positions while keeping net positions unchanged and it is part of the financial legislation in the US (Dodd-Frank Act) and in Europe (European Market Infrastructure Regulation).  We derive necessary structural conditions for portfolio compression to be harmful and discuss policy implications. In particular, we show that the potential danger of portfolio compression comes from defaults of firms that conduct portfolio compression. If no such defaults occur, then portfolio compression reduces systemic risk.          

 

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Title

Martingale Optimal Transport in Robust Finance
 

Abstract

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Without assuming any probabilistic price dynamics, we consider a 
frictionless financial market given by the Skorokhod space, on which 
some financial options are liquidly traded. In this model-free setting 
we show various pricing-hedging dualities and the analogue of the 
fundamental theorem of asset pricing. For this purpose we study the 
corresponding martingale optimal transport (MOT) problem: We obtain a 
dual representation of the Kantorovich functional (super-replication 
functional) defined for functions (financial derivatives) on the 
Skorokhod space using quotient sets (hedging sets). Our representation 
takes the form of a Choquet capacity generated by martingale measures 
satisfying additional constraints to ensure compatibility with the 
quotient sets. The talk is based on a joint work with Patrick 
Cheridito, Matti Kiiski and H. Mete Soner.

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Title

A Dual Characterisation of Regulatory Arbitrage for Coherent Risk Measures

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Abstract

We revisit portfolio selection in a one-period financial market under a coherent risk measure constraint, the most prominent example being Expected Shortfall (ES). Unlike in the case of classical mean-variance portfolio selection, it can happen that no efficient portfolios exist. We call this situation regulatory arbitrage. We then show that the absence of regulatory arbitrage is intimately linked to the interplay between the set of equivalent martingale measures (EMMs) for the discounted risky assets and the set of absolutely continuous measures in the dual characterisation of the risk measure. In the special case of ES, our result shows that the market does not admit regulatory arbitrage for ES at confidence level $\alpha$ if and only if there exists an EMM $Q \approx P$ such that $\Vert \frac{dQ}{dP} \Vert_\infty < \frac{1}{\alpha}$.

The talk is based on joint work with my PhD student Nazem Khan.

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Title

Equilibrium asset pricing with frictions

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Abstract

We study how the prices of assets depend on their “liquidity”, that is, the ease with which they can be traded. We show that equilibrium prices and the corresponding optimal trading strategies can be characterised by systems of coupled forward-backward SDEs. We outline some first wellposedness results and discuss explicit formulas that arise in the limit of large liquidity. 

 

The talk is based on joints works with Agostino Capponi, Lukas Gonon, Martin Herdegen, Dylan Possamai, and Xiaofei Shi.

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Title

Minimising the shuttle/commute time

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Abstract

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We consider the problem of choosing a diffusion's drift so as to minimise the expected time to commute from zero to 1 and back again.

We solve this first as a static problem and then (in  a suitable sense) dynamically.

Title

The Optimal Equity Selling Price with Endogenous Drawdown

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Abstract

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In this paper, we propose the endogenous drawdown in an investor's reward function. The endogenous drawdown is the difference between the underlying process and its maximum related process. We find the optimal selling price is a function of the historical highest price, the weights of profit and loss in investor's reward function, and the characters of the underlying stochastic process. With the data of the S&P 500 Index and SSE Composite Index, we calculate the numerical solution of the optimal selling price with consideration of endogenous drawdown. Through the out-sample test, this optimal selling price performs well to sell before the price drops sharply.

Title

A Fourier-based Picard-iteration approach for a class of McKean-Vlasov SDEs with Lévy jumps

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Abstract

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We consider a prototype class of Lévy-driven stochastic  differential equations (SDEs) with McKean-Vlasov (MK-V) interaction in the drift coefficient. It is assumed that the drift coefficient is affine in the state variable, and only measurable in the law of the solution. We study the equivalent functional fixed-point equation for the unknown time-dependent coefficients of the associated linear Markovian SDE. By proving a contraction property for the functional map in a suitable normed space, we infer existence and uniqueness results for the MK-V SDE, and derive a discretized Picard iteration scheme that approximates the law of the solution through its characteristic function. Numerical illustrations show the effectiveness of our method, which appears to be appropriate to handle the multi-dimensional setting. This is a joint work with Stefano Pagliarani.

Title

Talagrand Concentration Inequalities for Stochastic Heat-Type Equations  under Uniform Distance

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Abstract

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In this paper, we established a  quadratic transportation cost inequality under the uniform/maximum norm for solutions of stochastic heat equations driven by multiplicative space-time white noise. The proof is  based on a new inequality we obtained for the moments of the stochastic convolution with respect to space-time white noise, which is of independent interest. The solutions of such stochastic partial differential equations are typically not semimartingales on the state space.

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The talk by Tusheng Zhang has been CANCELLED.

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Title

TBA

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Abstract

TBA

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This seminar session has been postponed due to the Covid-19 crisis.

It will take place on the 25th of  March 2021.

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