### Note: the risk seminar has been changed to the Columbia Mathematical Finance Seminar 9/4/2012

### Semester Schedule

**Risk Seminar - Spring 2012**

**Seminars are on Thursday
Time: 4:10 - 5:25 PM
**

**Location:
Columbia University, 1255 Amsterdam Avenue, Room 903 SSW, 9th Floor**

CUNY Graduate Center, 365 Fifth Avenue, Room 4214.03, 4th Floor

Organizers: Olympia Hadjiliadis,
Gerardo Hernandez-del-Valle, Hongzhong Zhang

Thursday, Jan 19, 4:10-5:25pm

Speaker: Prof. Maria Victoria, Columbia University

Title: Enterprise Risk Management and Modelling: Solvency II issues

Abstract: Solvency II establishes a new European solvency system and an enterprise risk management process that takes more into account the real risks that insurance companies, reinsurers and captives companies are facing.

Solvency II is based upon three pillars or principles. Pillar I concerns the valuation of assets, liabilities and quantitative requirements for measuring capital adequacy. Pillar II regards the supervisory process and includes the review of risk management practices and ORSA (Own Risk Solvency Assessment Process). Pillar III involves the transparency and reporting requirements. Its methodology and structure is that of Base II /III, though of course adapted to the insurance sector, whereas Basel II/III applied to the banking industry. Not only did SII cause major changes in the European but also in the US insurance industry. It immediately impacts companies with direct compliance requirements such as US subsidiaries of European parents or US parents with European subsidiaries.

The aim of this presentation is twofold: briefly introducing SII and its latest updates and discussing some of the most important issues insurance companies have to deal with in this new framework. These issues concern subsequently:

1. Internal model, partial model or standard model?: Diversification and Dependence Risks.

2. Issues related to Own Risk Solvency Assessment

3. Connection between the Enterprise Risk Management Process and Solvency II: Vision of rating agencies

4. Comparison between Solvency II and US regulation

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Thursday, Jan 26, 4:10-5:25pm

Columbia SSW 903

Speaker: Prof. Stephen Figlewski, New York University

Title: Using Index Options to Learn about Price Expectations and
Risk Preferences in the Stock Market

Abstract:

Market prices for options on a broad stock market index reflect investors' assessment of the probability distribution for the level of the index on expiration day, adjusted for the market's tolerance for bearing risk. This information is contained in the "risk neutral probability distribution" (RND), which can be extracted from option price quotes in the market. The presentation will describe research applying this technology to the U.S. stock market, including some or all of the following:

1. How the risk neutral density is extracted from option prices;

2. How the RND changes from day to day and from minute to minute within a day as the underlying stock market moves;

3. How the RND behaved during relatively calm periods in 2006 and 2007, and during the financial crisis of 2008;

4. How the public release of the Federal Reserve's interest rate target is incorporated into market prices.

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Thursday, Feb 2, 4:10-5:25pm

Speaker: Prof. Marcel Nutz, Columbia University

Title: Pathwise Construction of Stochastic Integrals

Abstract:

We propose a method to define continuous-time wealth processes (i.e. stochastic integrals) for agents trading in a financial market under (non-dominated) model uncertainty. Path-by-path, and without referring to a probability measure, we construct a sequence of Lebesgue-Stieltjes integrals whose medial limit coincides with the usual stochastic integral under essentially any probability measure such that the integrator is a semimartingale.

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Thursday, Feb 8, 4-5pm

Speaker: Prof. Ren-raw Chen, Fordham University

Title: Valuing a Liquidity Discount

Abstract: PDF.

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Thursday, Feb 16, 4:10-5:25pm

Columbia SSW 903

Speaker: Prof. Agostino Capponi, Purdue University

Title: Dynamic Portfolio Optimization with a Defaultable Security and Regime Switching

Joint work with J.E.Figueroa Lopez

Abstract:

In this talk, we consider a portfolio optimization problem in a market where the investor can dynamically allocate her wealth among a defaultable bond, a stock, and a money market account. The market coefficients are assumed to depend on the regime in place, which is modeled by a finite state continuous time Markov process. By separating the utility maximization problem into a pre-default and post-default component, we deduce two coupled Hamilton-Jacobi-Bellman equations for the post and pre-default optimal value functions, and show a novel verification theorem for their solutions. We obtain explicit constructions of value functions and investment strategies for investors with logarithmic and Constant Relative Risk Aversion (CRRA) utilities, and provide a precise characterization of the directionality of the bond investment strategies in terms of corporate returns, forward rates, and expected recovery at default. We illustrate the dependence of the optimal strategies on time, losses given default, and risk aversion level of the investor through a detailed economic analysis..

Thursday, Feb 16, 5:30-6:30pm

Columbia SSW 903

Title: On Pricing Contingent Capital Notes

Abstract:

A bank's stock price is modeled as a call option on the spread of random assets over random liabilities. The logarithm of assets and liabilities are jointly modeled as driven by four variance gamma processes and this model is estimated by calibrating to quoted equity options seen as compound spread options. On defining riskweighted assets as asset value less the bid price plus the ask price of liabilities less the liability value we endogenize capital adequacy ratios following the methods of conic finance for the bid and ask prices. All computations are illustrated on CSGN.VX, ADRed into USD on March 29 2011.

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Thursday, Feb 23

Speaker: Prof. Alexander Tartakovsky, University of Southern California

Title: Recent Advances in Quickest Changepoint Detection

Abstract:

Changepoint problems deal with detecting (usually abrupt) changes in a process. The gist of the sequential changepoint problem is to design a detection procedure that minimizes the detection delay of a change subject to constraints on the risk associated with false alarms. I will present a detailed overview of the field with the focus on recent advances. Some open problems will also be discussed. I will address Bayesian, generalized Bayesian, and minimax optimality criteria. Not only conventional iid models but also general non-iid stochastic models will be addressed.

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Thursday, March 1, 4:10-5:25pm

903 SSW, Columbia

Speaker: Mr Vincenzo Ferrazzano, Technische Universität München

Title: TBA

Abstract:

Many real world turbulent flows, e.g. boundary layer atmospheric turbulence, are characterized by a high Reynolds number (fully developed turbulence). We consider the class of moving average processes, as already considered by Barndorff-Nielsen and Schimegl, as model for turbulence. In this class of processes the kernel function is responsible for the autocorrelation structure, which in the turbulence case should be universal, accordingly to the Kolmogorov's theory. Then there is an intrinsic interest in estimating it. We present an estimator for the kernel function and we show results for the class of process with regularly varying spectral density at infinity, which include the class of CARMA processes. We conclude with a small simulation study and a real data example.

This is based on a joint work with Claudia Klüppelberg and Peter Brockwell.

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Thursday, March 8, 4:10-5:25pm

903 SSW, Columbia

Speaker: Prof. Ioannis Karatzas, Columbia University

Title: Martingale approach to stochastic differential games of control and stopping

Abstract:

In the early 1970's Vic Benes, Mark Davis, Ty Duncan, Ray Rishel and Pravin Varaiya laid the foundations for what became known as the martingale approach to stochastic control. Their work was in the spirit of a similar approach that had been developed by J.L. Snell for optimal stopping twenty years earlier. We develop a similar approach for stochastic differential games of control and stopping, and for optimal stopping in the context of a decision maker who uses convex risk measures to evaluate future rewards. (Joint work with Ingrid-Mona Zamfirescu, Erhan Bayraktar and Song Yao.)

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Thursday, March 22, 4:10-5:25pm

Columbia 903 SSW

Speaker: Prof. Dharma Kwon, UIUC

Title: Employee Retention and Job Assignment Strategies of Entrepreneurial Firms under Uncertainty in Employee Capability

Abstract:

We study the employee retention and job assignment strategy of growth-oriented entrepreneurial firms in which the employee's capability is unknown to both the firm and the employee. As the employee performs his task, both the firm and the employee update their common belief about the employee's capability based on the noisy profit stream from the employee's performance. The firm seeks to dismiss low-capability employees while high-capability employees seek to leave the firm for higher compensation. We model this situation as a real options game between the firm and the employee, and we obtain a Markov perfect equilibrium (MPE) characterized by the employment termination strategies of the two players. In stark contrast to conventional real options models, a higher rate of learning can hurt both players when the employee's capability is sufficiently uncertain. This suggests that firms should assign employees with highly uncertain capabilities to tasks with high noise levels.

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Thursday, March 29, 4:10-5:25pm

903 SSW, Columbia

Speaker: Prof. Frank Riedel, Bielefeld University

Title: Market Breakdown and Indeterminacy under Model Uncertainty

Abstract:

We study a dynamic financial market with model (or "Knightian") uncertainty when agents use the inertia principle proposed by Bewley. We characterize efficient allocations and equilibria in abstract economies. In a second step, we study a mean--variance version of the model where agents face risk as well as (model) uncertainty. We show that trade occurs in the risky part of the market whereas trade in the uncertain assets breaks down when model uncertainty passes a certain threshold. We also show that equilibria with inertia are indeterminate so that equilibrium prices may fluctuate in a certain range around one "focal" equilibrium.

Downloadable paper.

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Thursday, April 5

Speaker: Professor Xin Guo, UC Berkely

Title: Economic default and Arcsine Law

Joint work with R. Jarrow of Cornell and A. de Larrard of Paris VI.

Abstract:

This paper develops a structural credit risk model to characterize the difference between the economic and recorded default times for a firm. Recorded default occurs when default is recorded in the legal system. The economic default time is the last time when the firm is able to pay off its debt prior to the legal default time. It has been empirically documented that these two times are distinct (see Guo, Jarrow, and Lin (2008)). In our model, the probability distribution for the time span between economic and recorded defaults is analyzed, and is shown to follow a mixture of Arcsine Laws for some special cases. This is consistent with the results contained in Guo, Jarrow, and Lin. In addition, we show that the classical structural model is a limiting case of our model as the time period between debt repayment dates goes to zero. As a corollary, we show how the firm value process's parameters can be estimated using the tail index and correlation structure of the firm's return.

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Thursday, April 12

Speaker: Professor Johannes Muhle-Karbe, ETH Zurich

Title: Optimal investment with small transaction costs and general
stochastic opportunity sets.

Joint work with Jan Kallsen.

Abstract:

For an investor with constant absolute risk aversion, we informally derive the first-order asymptotics of the optimal investment strategy as the bid-ask spread becomes small. For general It\^o processes, the first order correction term is expressed in terms of the quadratic variation of the frictionless optimizer. This result allows to quantify the impact of, e.g., predictability and stochastic volatility on portfolio choice in the presence of transaction costs. Applied to an investor holding a random endowment, it also leads to a generalization of the asymptotic utility-based hedging strategies determined by Whalley and Wilmott (1997) for a constant opportunity set.

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Thursday, April 19

Speaker: Dr Stephan Sturm, Princeton University

Title: From Smile Wings to Market Risk Measures

Abstract:

The left tail of the implied volatility skew, coming from quotes on out-of-the-money put options, can be thought to reflect the market's assessment of the risk of a huge drop in stock prices. We analyze how this market information can be integrated into the theoretical framework of convex monetary measures of risk. In particular, we make use of indifference pricing by dynamic convex risk measures, which are given as solutions of backward stochastic differential equations (BSDEs), to establish a link between these two approaches to risk measurement. We derive a characterization of the implied volatility in terms of the solution of a nonlinear PDE and provide a small time-to-maturity expansion. This procedure allows to choose convex risk measures in a conveniently parametrized class, distorted entropic dynamic risk measures, such that the asymptotic volatility skew under indifference pricing can be matched with the market skew. This is joint work with Ronnie Sircar.

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Thursday, April 26

Speaker: Dr. Samuel Cohen, Oxford.

Title: TBA.

Abstract:

TBA

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