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A continuous optimization model for a joint problem of pricing and resource allocation

Mustapha Bouhtou, Guillaume Erbs (2009)

RAIRO - Operations Research

This paper investigates the problem of maximizing the revenue of a telecommunications operator by simultaneously pricing point-to-point services and allocating bandwidth in its network, while facing competition. Customers are distributed into market segments, i.e., groups of customers with a similar preference for the services. This preference is expressed using utility functions, and customers choose between the offers of the operator and of the competition according to their utility. We model...

An equilibrium model for electricity auctions

Juri Hinz (2003)

Applicationes Mathematicae

This work discusses the process of price formation for electrical energy within an auction-like trading environment. Calculating optimal bid strategies of power producers by equilibrium arguments, we obtain the corresponding electricity price and estimate its tail behavior.

Analytical approximation of the transition density in a local volatility model

Stefano Pagliarani, Andrea Pascucci (2012)

Open Mathematics

We present a simplified approach to the analytical approximation of the transition density related to a general local volatility model. The methodology is sufficiently flexible to be extended to time-dependent coefficients, multi-dimensional stochastic volatility models, degenerate parabolic PDEs related to Asian options and also to include jumps.

Arbitrage for simple strategies

Agnieszka Rygiel, Łukasz Stettner (2012)

Applicationes Mathematicae

Various aspects of arbitrage on finite horizon continuous time markets using simple strategies consisting of a finite number of transactions are studied. Special attention is devoted to transactions without shortselling, in which we are not allowed to borrow assets. The markets without or with proportional transaction costs are considered. Necessary and sufficient conditions for absence of arbitrage are shown.

Auctions with Untrustworthy Bidders

Braynov, Sviatoslav, Pavlov, Radoslav (2007)

Serdica Journal of Computing

The paper analyzes auctions which are not completely enforceable. In such auctions, economic agents may fail to carry out their obligations, and parties involved cannot rely on external enforcement or control mechanisms for backing up a transaction. We propose two mechanisms that make bidders directly or indirectly reveal their trustworthiness. The first mechanism is based on discriminating bidding schedules that separate trustworthy from untrustworthy bidders. The second mechanism is a generalization of...

Conditional distributions, exchangeable particle systems, and stochastic partial differential equations

Dan Crisan, Thomas G. Kurtz, Yoonjung Lee (2014)

Annales de l'I.H.P. Probabilités et statistiques

Stochastic partial differential equations (SPDEs) whose solutions are probability-measure-valued processes are considered. Measure-valued processes of this type arise naturally as de Finetti measures of infinite exchangeable systems of particles and as the solutions for filtering problems. In particular, we consider a model of asset price determination by an infinite collection of competing traders. Each trader’s valuations of the assets are given by the solution of a stochastic differential equation,...

Constrained portfolio liquidation in a limit order book model

Aurélien Alfonsi, Antje Fruth, Alexander Schied (2008)

Banach Center Publications

We consider the problem of optimally placing market orders so as to minimize the expected liquidity costs from buying a given amount of shares. The liquidity price impact of market orders is described by an extension of a model for a limit order book with resilience that was proposed by Obizhaeva and Wang (2006). We extend their model by allowing for a time-dependent resilience rate, arbitrary trading times, and general equilibrium dynamics for the unaffected bid and ask prices. Our main results...

Dynamic programming for an investment/consumption problem in illiquid markets with regime-switching

Paul Gassiat, Fausto Gozzi, Huyên Pham (2015)

Banach Center Publications

We consider an illiquid financial market with different regimes modeled by a continuous time finite-state Markov chain. The investor can trade a stock only at the discrete arrival times of a Cox process with intensity depending on the market regime. Moreover, the risky asset price is subject to liquidity shocks, which change its rate of return and volatility, and induce jumps on its dynamics. In this setting, we study the problem of an economic agent optimizing her expected utility from consumption...

Entropic Conditions and Hedging

Samuel Njoh (2007)

ESAIM: Probability and Statistics

In many markets, especially in energy markets, electricity markets for instance, the detention of the physical asset is quite difficult. This is also the case for crude oil as treated by Davis (2000). So one can identify a good proxy which is an asset (financial or physical) (one)whose the spot price is significantly correlated with the spot price of the underlying (e.g. electicity or crude oil). Generally, the market could become incomplete. We explicit exact hedging strategies for exponential...

Hedging in complete markets driven by normal martingales

Youssef El-Khatib, Nicolas Privault (2003)

Applicationes Mathematicae

This paper aims at a unified treatment of hedging in market models driven by martingales with deterministic bracket M , M t , including Brownian motion and the Poisson process as particular cases. Replicating hedging strategies for European, Asian and Lookback options are explicitly computed using either the Clark-Ocone formula or an extension of the delta hedging method, depending on which is most appropriate.

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