## SEM217: Haosui (Kevin) Duanmu, UC Berkeley: Nonstandard Analysis and its Application to Markov Processes

Tuesday, September 18th @ 11:00-12:30 PM

**Nonstandard Analysis and its Application to Markov Processes**

**Haosui (Kevin) Duanmu, UC Berkeley**

Nonstandard analysis, a powerful machinery derived from mathematical logic, has had many applications in probability theory as well as stochastic processes. Nonstandard analysis allows construction of a single object - a hyperfinite probability space - which satisfies all the first order logical properties of a finite probability space, but which...

## Haosui (Kevin) Duanmu, UC Berkeley: Nonstandard Analysis and its Application to Markov Processes

Nonstandard analysis, a powerful machinery derived from mathematical logic, has had many applications in probability theory as well as stochastic processes. Nonstandard analysis allows construction of a single object - a hyperfinite probability space - which satisfies all the first order logical properties of a finite probability space, but which can be simultaneously viewed as a measure-theoretical probability space via the Loeb construction. As a consequence, the hyperfinite/measure duality has proven to be particularly in porting discrete results into their continuous settings. In this...

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We consider the optimal execution of a book of options when market impact is a driver of the option price. We aim at minimizing the mean-variance risk criterion for a given market impact function. First, we develop a framework to justify the choice of our market impact function. Our model is inspired from Leland’s option replication with transaction costs where the market impact is directly part of the implied volatility function. The option price is then expressed through a Black– Scholes-like PDE with a modified implied volatility directly dependent on the market impact. We set up a...

## Tingyue Gan, UC Berkeley: Asymptotic Spectral Analysis of Markov Chains with Rare Transitions: A Graph-Algorithmic Approach

Parameter-dependent Markov chains with exponentially small transition rates arise in modeling complex systems in physics, chemistry, and biology. Such processes often manifest metastability, and the spectral properties of the generators largely govern their long-term dynamics. In this work, we propose a constructive graph-algorithmic approach to computing the asymptotic estimates of eigenvalues and eigenvectors of the generator. In particular, we introduce the concepts of the hierarchy of Typical Transition Graphs and the associated sequence of Characteristic Timescales. Typical Transition...

## Michael Ohlrogge, Stanford University: Bankruptcy Claim Dischargeability and Public Externalities: Evidence from a Natural Experiment

In 2009, the Seventh Circuit ruled in *U.S. v. Apex Oil* that certain types of injunctions requiring firms to clean up previously released toxic chemicals were not dischargeable in bankruptcy. This was widely perceived to represent a split with Sixth Circuit precedent, although Supreme Court cert was denied. Numerous legal commentators wrote of the significance of this decision in strengthening incentives for firms, and their creditors, to reduce the likelihood of costly environmental damage that would no longer be dischargeable in the event of bankruptcy. I show using difference in...

## Xiang Zhang, SWUFE: Proliferation of Anomalies and Zoo of Factors – What does the Hansen–Jagannathan Distance Tell Us?

Recent research finds that prominent asset pricing models have mixed success in evaluating the cross-section of anomalies, which highlights proliferation of anomalies and zoo of factors. In this paper, I investigate that how is the relative pricing performance of these models to explain anomalies, when comparing their misspecification errors– the Hansen–Jagannathan (HJ) distance measure. I find that a traded-factor model dominates others in a specific anomaly by incorporating the multiple HJ distance comparing inference. However, different from the current research of Barillas and Shanken...

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## Chi Zhang, Kamyar Kaviani, Nikita Vemuri, and Simon Walter (UC Berkeley) - Putting the 'I' in IPO

As an alternative to traditional loans, young people could issue securities that pay dividends that depend on their future financial success in life. This type of a personal IPO is especially desirable for young people, who for example may need money for a college education, because it allows them to shift the risk of repayment to investors who bet on their future success, unlike in a traditional loan setting. In this seminar we will report a framework for estimating an indicative IPO price for individuals and placing the securities with investors. We will also demo an app that is designed...

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