Aleš Černý

I am a professor in the Finance Faculty at the Bayes Business School. I grew up and received my education in Czechoslovakia, graduating in Mathematical Engineering at the Czech Technical University in Prague. Subsequently I studied doctoral economics at CERGE, Charles University in Prague and obtained a PhD in Economics from the University of Warwick under the supervision of Marcus Miller and Stewart Hodges. Before joining Bayes, I worked several years at the Imperial College Business School. I am also a visiting professor of mathematics at the Comenius University in Bratislava.

My work on asset pricing in incomplete markets ranges from axiomatic foundations to general theory of expected utility optimization, to practical applications of mean–variance preferences and their monotonization. This work has generated some purely mathematical results in linear algebra (characterisation of oblique projectors) and stochastic analysis (semimartingale decompositions; stochastic jump integral). Early on in my career, I have worked with David Miles on optimal life cycle asset allocation with particular focus on pension and real estate investment. I have also been interested in optimal asset liquidation with endogenous liquidation horizon.

Research Interests

My current research interests lie on the interface between stochastic analysis, convex optimization, and utility theory. It turns out that many transformations of stochastic processes can be fruitfully described by “predictable variations”, where roughly speaking a new process  is obtained by a predictable function   acting on the increments of an existing process , i.e.,
Thinking of  as a cumulative yield on a portfolio, , and  as a utility function, we can think of  as the realized cumulative local utility. The drift rate of  can then be understood as the “local expected utility”.  Maximization of local expected utility leads to a natural question whether the optimizer, say , integrates  in the sense of stochastic integration theory. More broadly, there is some hope that by redoing the classical utility maximization theory locally, one may be able to say more about globally optimal strategies for expected utility.  Expected utility and related criteria are a key tool for decision making in incomplete market settings, such as optimal hedging and risk management.

Expertise Details

As an applied mathematician and an economist, I have always played catch-up with formal mathematics. Over the years, I have been instructed by my colleagues and collaborators in various aspects of convex analysis; Orlicz space theory; functional analysis; linear algebra; stochastic analysis; and stochastic control theory. I am constantly developing my understanding of these areas vis-à-vis applications in financial economics.

My strongest skill probably lies in applied mathematical modelling, i.e., in the ability to take a real-world problem, convert it reasonably faithfully into a mathematical model, perform computations in the model, and appropriately interpret the results in the form of action recommendations.

Expertise Details

Stochastic analysis; Convex optimization; and Utility theory.