42 citations · 105 across the 19 of their papers we have counts for
25 papers
Rough PDEs for local stochastic volatility models
Peter Bank, Christian Bayer, Peter K. Friz +1
In this work, we introduce a novel pricing methodology in general, possibly non-Markovian local stochastic volatility (LSV) models. We observe that by conditioning the LSV dynamics…
Optimal execution and speculation with trade signals
Peter Bank, Álvaro Cartea, Laura Körber
We propose a price impact model where changes in prices are purely driven by the order flow in the market. The stochastic price impact of market orders and the arrival rates of lim…
Optimal investment with a noisy signal of future stock prices
Peter Bank, Yan Dolinsky
We consider an investor who is dynamically informed about the future evolution of one of the independent Brownian motions driving a stock's price fluctuations. With linear temporar…
Merton's optimal investment problem with jump signals
Peter Bank, Laura Körber
This paper presents a new framework for Merton's optimal investment problem which uses the theory of Meyer -fields to allow for signals that possibly warn the investor about imp…
What if we knew what the future brings? Optimal investment for a frontrunner with price impact
Peter Bank, Yan Dolinsky, Miklós Rásonyi
In this paper we study optimal investment when the investor can peek some time units into the future, but cannot fully take advantage of this knowledge because of quadratic transac…
A Note on Utility Indifference Pricing with Delayed Information
Peter Bank, Yan Dolinsky
We consider the Bachelier model with information delay where investment decisions can be based only on observations from time units before. Utility indifference prices are st…
On a Stochastic Representation Theorem for Meyer-measurable Processes and its Applications in Stochastic Optimal Control and Optimal Stopping
Peter Bank, David Besslich
In this paper we study a representation problem first considered in a simpler version by Bank and El Karoui [2004]. A key ingredient to this problem is a random measure on the…
Modelling information flows by Meyer--fields in the singular stochastic control problem of irreversible investment
Peter Bank, David Besslich
In stochastic control problems delicate issues arise when the controlled system can jump due to both exogenous shocks and endogenous controls. Here one has to specify what the cont…
On Lenglart's Theory of Meyer-sigma-fields and El Karoui's Theory of Optimal Stopping
Peter Bank, David Besslich
We summarize the general results of El Karoui [1981] on optimal stopping problems for processes which are measurable with respect to Meyer--fields. Meyer--fields are due to L…
Scaling Limits for Super--replication with Transient Price Impact
Peter Bank, Yan Dolinsky
We prove a scaling limit theorem for the super-replication cost of options in a Cox--Ross--Rubinstein binomial model with transient price impact. The correct scaling turns out to k…
Photonic systems with two-dimensional landscapes of complex refractive index via time-dependent supersymmetry
Alonso Contreras-Astorga, Vit Jakubský
We present a framework for the construction of solvable models of optical settings with genuinely two-dimensional landscapes of refractive index. The solutions of the associated no…
Liquidity in Competitive Dealer Markets
Peter Bank, Ibrahim Ekren, Johannes Muhle-Karbe
We study a continuous-time version of the intermediation model of Grossman and Miller (1988). To wit, we solve for the competitive equilibrium prices at which liquidity takers' dem…
Optimal investment with transient price impact
Peter Bank, Moritz Voß
We introduce a price impact model which accounts for finite market depth, tightness and resilience. Its coupled bid- and ask-price dynamics induce convex liquidity costs. We provid…
Linear quadratic stochastic control problems with stochastic terminal constraint
Peter Bank, Moritz Voß
We study a linear quadratic optimal control problem with stochastic coefficients and a terminal state constraint, which may be in force merely on a set with positive, but not neces…
Super-Replication with Fixed Transaction Costs
Peter Bank, Yan Dolinsky
We study super--replication of contingent claims in markets with fixed transaction costs. This can be viewed as a stochastic impulse control problem with a terminal state constrain…
The Scaling Limit of Superreplication Prices with Small Transaction Costs in the Multivariate Case
Peter Bank, Yan Dolinsky, Ari-Pekka Perkkiö
Kusuoka [ Limit Theorem on Option Replication Cost with Transaction Costs, Ann. Appl. Probab. 5, 198--221, (1995).] showed how to obtain non-trivial scaling limits of superreplicat…
Hedging with Temporary Price Impact
Peter Bank, Mete Soner, Moritz Voß
We consider the problem of hedging a European contingent claim in a Bachelier model with transient price impact as proposed by Almgren and Chriss. Following the approach of Rogers…
Super-replication with nonlinear transaction costs and volatility uncertainty
Peter Bank, Yan Dolinsky, Selim Gökay
We study super-replication of contingent claims in an illiquid market with model uncertainty. Illiquidity is captured by nonlinear transaction costs in discrete time and model unce…
Convex duality for stochastic singular control problems
Peter Bank, Helena Kauppila
We develop a general theory of convex duality for certain singular control problems, taking the abstract results by Kramkov and Schachermayer (1999) for optimal expected utility fr…
The stochastic field of aggregate utilities and its saddle conjugate
Peter Bank, Dmitry Kramkov
We describe the sample paths of the stochastic field of aggregate utilities parameterized by Pareto weights and total cash amounts and stocks' quantities $…
Superreplication when trading at market indifference prices
Peter Bank, Selim Gökay
We study superreplication of European contingent claims in discrete time in a large trader model with market indifference prices recently proposed by Bank and Kramkov. We introduce…
Optimal Order Scheduling for Deterministic Liquidity Patterns
Peter Bank, Antje Fruth
We consider a broker who has to place a large order which consumes a sizable part of average daily trading volume. The broker's aim is thus to minimize execution costs he incurs fr…
On a stochastic differential equation arising in a price impact model
Peter Bank, Dmitry Kramkov
We provide sufficient conditions for the existence and uniqueness of solutions to a stochastic differential equation which arises in a price impact model. These conditions are stat…
A model for a large investor trading at market indifference prices. II: Continuous-time case
Peter Bank, Dmitry Kramkov
We develop from basic economic principles a continuous-time model for a large investor who trades with a finite number of market makers at their utility indifference prices. In thi…