Stochastics: a workshop on diffusion processes, BSDEs, optimal control, and risks

Föreläsningarna tar upp ämnen med olika, intressanta perspektiv, bland annat:

• Backward stochastic differential equations
• Optimal control
• Malliavin calculus
• Mean fields
• Statistics and finance

Program

13:00-13:40 Bernt Øksendal, Universitetet i Oslo, Norge
Optimal control of stochastic Volterra integral equations

13:40-14:00 Badr-eddine Berrhazi, Université Ibn Tofaïl, Marocko / Linnéuniversitetet
Reflected backward doubly stochastic differential equations with discontinuous barrier

14:00-14:15 Paus

14:15-14:55 Erik Ekström, Uppsala universitet
Bayesian sequential least-squares estimation of the drift of a Wiener process

14:55-15:15 Fatima-Ezzahra Farah, Université Cadi Ayyad, Marocko / Linnéuniversitetet
Weyl multifractional Ornstein-Uhlenbeck process mixed with a Gamma distribution

15:15-15:30 Paus

15:30-16:00 Nacira Agram, Université de Biskra, Algeriet
Dynamic risk measures for BSVIEs and semimartingale issues

16:00-16:20 Ximei Wang, KTH
Sovereign credit rating based on the international trade and financial integration network

16:20-16:35 Paus

16:35-17:15 Boualem Djehiche, KTH
On a class of entropic backward SDEs related to risk-sensitive optimal mean-field control of Markov chains

Workshopen organiseras av forskargruppen Stochastic Analysis and Stochastic Processes, i synnerhet av Badr-eddine Berrhazi och Fatima-Ezzahra Farah.

Ladda hem affischen för workshopen.

Abstract

Nacira Agram: Dynamic risk measures for BSVIEs and semimartingale issues

Stochastic Volterra integral equations are a special type of integral equation. They represent interesting models for stochastic dynamics with memory, with applications to e.g. engineering, biology and finance. Backward stochastic Volterra integral equations are also interesting because they may represent recursive utilities and convex dynamic risk measures. We should also emphasise that a Convex Risk Measure is a better measure of risk than the classical Value at Risk (Var), because Var is not convex. The importance of convexity is that it means that diversification reduces the risk. Every risk measure should have that property. Since backward stochastic Volterra integral equations are not in general semimartingales, we will discuss some particular cases.

Badr-eddine Berrhazi: Reflected backward doubly Stochastic Differential Equations with Discontinuous Barrier

In this work we investigate reflected backward doubly stochastic differential equations (RBDSDEs) with a lower not necessarily right-continuous obstacle. First we establish the existence and uniqueness of a solution to RBDSDEs with Lipschitz drivers. In the second part we present a comparison theorem and we prove existence of a minimal solution to RBDSDEs with continuous driver.

Boualem Djehiche: On a class of entropic backward SDEs related to risk- sensitive optimal mean-field control of Markov chains.

I will review existence and uniqueness of solutions to a class of entropic backward SDEs that appear in the characterization  of risk- sensitive optimal mean-field controls of Markov chains.

Erik Ekström: Bayesian sequential least-squares estimation of the drift of a Wiener process

Given a Wiener process with unknown and unobservable drift, we seek to estimate this drift as quickly as possible, in the presence of a quadratic penalty for the estimation error and of a linear cost per unit time of observation. In a Bayesian framework, this question reduces to choosing judiciously a stopping time for an appropriate diffusion process in natural scale; we provide structural properties of the solution for the corresponding problem of optimal stopping.

Fatima-Ezzahra Farah: Weyl multifractional Ornstein-Uhlenbeck process mixed with a Gamma distribution

The aim of this paper is to study the asymptotic behavior of the aggregated Weyl multifractional Ornstein-Uhlenbeck processes mixed with Gamma distribution random variables. This allows us to introduce a process called Gamma-mixed Weyl multifractional Ornstein-Uhlenbeck process and study its elementary properties such as Hausdorff dimension, locally self-similarity and short range dependence. The asymptotic behavior of our process is also studied and it approaches the multifractional Brownian motion.

Bernt Øksendal: Optimal control of stochastic Volterra integral equations

We study optimal control of stochastic Volterra integral equations (SVIE) with jumps by using Hida-Malliavin calculus.

1. We give conditions under which there exists a unique solution of such equations.
2. Then we prove both a sufficient maximum principle (a verification theorem) and a necessary maximum principle via Hida-Malliavin calculus.
3. As an application we solve a problem of optimal consumption from a cash flow modelled by an SVIE.

The talk is based on joint work with Nacira Agram and Samia Yakhlef, University of Biskra, Algeria.

Ximei Wang​: Sovereign credit rating based on the international trade and financial integration network

Sovereign credit ratings are used to assess the ability of a government's ability and willingness in meeting their financial obligations on time. In this talk, we analyze probability of default of countries with the international trade and financial integration network information. The combination of both binary and weighted analysis method provide an comprehensive insight on the topologies structure and properties for the network.  Several centrality metrics as well as the degree distribution for the networks have been calculated for around 180 countries from 2010 to 2017. The study results show that high-income countries with vigorous economic trading links are more clustered and usually have a higher credit ratings. Besides, the importance ranks of the countries explain how the financial contagion happens in a worldwide range.