Christoph Czichowsky

• Professor (Associate) at London School of Economics and Political Science

We revisit the classical topic of quadratic and linear mean-variance equilibria with both financial and real assets. The novelty of our results is that they are the first allowing for equilibrium prices driven by general semimartingales and hold in discrete as well as continuous time. For agents with quadratic utility functions, we provide necessar...

The paper investigates quadratic hedging in a semimartingale market that does not necessarily contain a risk-free asset. An equivalence result for hedging with and without numeraire change is established. This permits direct computation of the optimal strategy without choosing a reference asset and/or performing a numeraire change. New explicit exp...

We consider robust utility maximisation in continuous-time financial markets with proportional transaction costs under model uncertainty. For this, we work in the framework of Chau and R\'asonyi (2019), where robustness is achieved by maximising the worst-case expected utility over a possibly uncountable class of models that are all given on the sa...

The law of one price (LOP) broadly asserts that identical financial flows should command the same price. This paper uncovers a new mechanism through which LOP can fail in a continuous-time $L^2(P)$ setting without frictions, namely `trading from just before a predictable stopping time', which surprisingly identifies LOP violations even for continuo...

The paper investigates quadratic hedging in a general semimartingale market that does not necessarily contain a risk-free asset. An equivalence result for hedging with and without numeraire change is established. This permits direct computation of the optimal strategy without choosing a reference asset and/or performing a numeraire change. New expl...

The aim of this short note is to establish a limit theorem for the optimal trading strategies in the setup of the utility maximization problem with proportional transaction costs. This limit theorem resolves the open question from [4]. The main idea of our proof is to establish a uniqueness result for the optimal strategy. The proof of the uniquene...

The aim of this short note is to establish a limit theorem for the optimal trading strategies in the setup of the utility maximization problem with proportional transaction costs. This limit theorem resolves the open question from [4]. The main idea of our proof is to establish a uniqueness result for the optimal strategy. Surprisingly, up to date,...

This paper presents findings from a case study on the impact of high stakes oral performance assessment on third year mathematics students’ approaches to learning (Entwistle & Ramsden, 1983). We choose oral performance assessment as this mode of assessment differs substantially from written exams for its dialogic nature and because variation of ass...

This paper presents findings from a case study on the impact of high stakes oral performance assessment on third year mathematics students’ approaches to learning (Entwistle & Ramsden, 1983). We choose oral performance assessment as this mode of assessment differs substantially from written exams for its dialogic nature and because variation of ass...

as this mode of assessment differs substantially from written exams for its dialogic nature and because variation of assessment methods is seen to be very important in an otherwise very uniform assessment diet. We found that students perceived the assessment to require conceptual understanding over memory and were more likely to employ revision str...

We continue the analysis of our previous paper (Czichowsky/Schachermayer/Yang 2014) pertaining to the existence of a shadow price process for portfolio optimisation under proportional transaction costs. There, we established a positive answer for a continuous price process $S=(S_t)_{0\leq t\leq T}$ satisfying the condition $(NUPBR)$ of "no unbounde...

We continue the analysis of our previous paper (Czichowsky/Schachermayer/Yang 2014) pertaining to the existence of a shadow price process for portfolio optimisation under proportional transaction costs. There, we established a positive answer for a continuous price process $S=(S_t)_{0\leq t\leq T}$ satisfying the condition $(NUPBR)$ of "no unbounde...

While absence of arbitrage in frictionless financial markets requires price processes to be semimartingales, non-semimartingales can be used to model prices in an arbitrage-free way, if proportional transaction costs are taken into account. In this paper, we show, for a class of price processes which are not necessarily semimartingales, the existen...

In a financial market with a continuous price process and proportional transaction costs we investigate the problem of utility maximization of terminal wealth. We give sufficient conditions for the existence of a shadow price process, i.e.~a least favorable frictionless market leading to the same optimal strategy and utility as in the original mark...

For portfolio optimisation under proportional transaction costs, we provide a duality theory for general cadlag price processes. In this setting, we prove the existence of a dual optimiser as well as a shadow price process in a generalised sense. This shadow price is defined via a "sandwiched" process consisting of a predictable and an optional str...

For portfolio choice problems with proportional transaction costs, we discuss whether or not there exists a shadow price, i.e., a least favorable frictionless market extension leading to the same optimal strategy and utility. By means of an explicit counter-example, we show that shadow prices may fail to exist even in seemingly perfectly benign sit...

Given a sequence $(M^n)^\infty_{n=1}$ of non-negative martingales starting at $M^n_0=1$ we find a sequence of convex combinations $(\widetilde{M}^n)^\infty_{n=1}$ and a limiting process $X$ such that $(\widetilde{M}^n_\tau)^\infty_{n=1}$ converges in probability to $X_\tau$, for all finite stopping times $\tau$. The limiting process $X$ then is an...

We study mean-variance hedging under portfolio constraints in a general semimartingale model. The constraints are formulated via predictable correspondences, meaning that the trading strategy is restricted to lie in a closed convex set which may depend on the state and time in a predictable way. To obtain the existence of a solution, we first estab...

The Markowitz problem consists of finding in a financial market a self-financing trading strategy whose final wealth has maximal mean and minimal variance. We study this in continuous time in a general semimartingale model and under cone constraints: Trading strategies must take values in a (possibly random and time-dependent) closed cone. We first...

It is well known that mean-variance portfolio selection is a time-inconsistent optimal control problem in the sense that it does not satisfy Bellman's optimality principle and therefore the usual dynamic programming approach fails. We develop a time- consistent formulation of this problem, which is based on a local notion of optimality called local...

Let S be an ℝ d -valued semimartingale and (ψ n ) a sequence of C-valued integrands, i.e. predictable, S-integrable processes taking values in some given closed set C(ω, t) ⊆ ℝ d which may depend on the state ω and time t in a predictable way. Suppose that the stochastic integrals (ψ n ⋅S) converge to X in the semimartingale topology. When can X...

Consider an \({\mathbb{R}}^{d}\)-valued semimartingale S and a sequence of \({\mathbb{R}}^{d}\)-valued S-integrable predictable processes H n valued in some closed convex set \(\mathcal{K}\subset {\mathbb{R}}^{d}\), containing the origin. Suppose that the real-valued sequence H n ⋅S converges to X in the semimartingale topology. We would like to kn...

For portfolio choice problems with proportional transaction costs, we discuss whether or not there exists a shadow price, i.e., a least favorable frictionless market extension leading to the same optimal strategy and utility. By means of an explicit counter-example, we show that shadow prices may fail to exist even in seemingly perfectly benign sit...