On Collisions of Brownian Particles (2008)
Ichiba, Tomoyuki, Karatzas, Ioannis
We examine the behavior of n Brownian particles diffusing on the real line, with bounded, measurable drift and bounded, piecewise continuous diffusion coefficients that depend on the current...
Testing Composite Hypotheses via Convex Duality (2008)
Rudloff, Birgit, Karatzas, Ioannis
We study the problem of testing composite hypotheses versus composite alternatives, using a convex duality approach. In contrast to classical results obtained by Krafft & Witting (1967), where...
Martingale approach to stochastic differential games of control and stopping (2008)
Karatzas, Ioannis, Zamfirescu, Ingrid-Mona
We develop a martingale approach for studying continuous-time stochastic differential games of control and stopping, in a non-Markovian framework and with the control affecting only the drift term of...
Diversity and relative arbitrage in equity markets (2008)
Fernholz, Robert, Karatzas, Ioannis, Kardaras, Constantinos
A financial market is called "diverse" if no single stock is ever allowed to dominate the entire market in terms of relative capitalization. In the context of the standard Ito-process model initiated...
The numeraire portfolio in semimartingale financial models (2008)
Karatzas, Ioannis, Kardaras, Constantinos
We study the existence of the numeraire portfolio under predictable convex constraints in a general semimartingale model of a financial market. The numeraire portfolio generates a wealth process,...
Optimal consumption from investment and random endowment in incomplete semimartingale markets (2007)
Karatzas, Ioannis, Zitkovic, Gordan
We consider the problem of maximizing expected utility from consumption in a constrained incomplete semimartingale market with a random endowment process, and establish a general existence and...
Adaptive Poisson disorder problem (2006)
Bayraktar, Erhan, Dayanik, Savas, Karatzas, Ioannis
We study the quickest detection problem of a sudden change in the arrival rate of a Poisson process from a known value to an unknown and unobservable value at an unknown and unobservable disorder...
Adaptive Poisson disorder problem (2006)
Bayraktar, Erhan, Dayanik, Savas, Karatzas, Ioannis
We study the quickest detection problem of a sudden change in the arrival rate of a Poisson process from a known value to an unknown and unobservable value at an unknown and unobservable disorder...
Atlas models of equity markets (2006)
Banner, Adrian D., Fernholz, Robert, Karatzas, Ioannis
Atlas-type models are constant-parameter models of uncorrelated stocks for equity markets with a stable capital distribution, in which the growth rates and variances depend on rank. The simplest such...
Atlas models of equity markets (2005)
Banner, Adrian D., Fernholz, Robert, Karatzas, Ioannis
Atlas-type models are constant-parameter models of uncorrelated stocks for equity markets with a stable capital distribution, in which the growth rates and variances depend on rank. The simplest such...
Optimal consumption from investment and random endowment in incomplete semimartingale markets (2003)
Karatzas, Ioannis, Žitković, Gordan
We consider the problem of maximizing expected utility from consumption in a constrained incomplete semimartingale market with a random endowment process, and establish a general existence and...
of American Put Options (2003)
Peter Carr, Robert Jarrow, Ravi Myneni, Leslie Greengard, David Heath, Steve Heston, ...
We derive alternative representations of the McKean equation for the value of the American put option. Our main result decomposes the value of an American put option into the corresponding European...
Optimal Stationary Linear Control of the Wiener Process. (2002)
Benes,Vaclav E., Karatzas,Ioannis
In this paper we consider the problem of stationary control of the stochastic differential equation where (W sub t) is a Wiener process on an underlying probability space. Two kinds of cost are...
The Controller-and-Stopper Game for a Linear Diffusion (2001)
Karatzas, Ioannis, Sudderth, William D.
Consider a process $X(\cdot) = {X(t), 0 \leq t < \infty}$ with values in the interval $I = (0, 1)$, absorption at the boundary points of $I$, and dynamics $$dX(t) = \beta(t)dt + \sigma(t)dW(t),\quad...
Generalized Neyman-Pearson lemma via convex duality (2001)
Cvitanic, Jaksa, Karatzas, Ioannis
We extend the classical Neyman-Pearson theory for testing composite hypotheses versus composite alternatives, using a convex duality approach, first employed by Witting. Results of Aubin and Ekeland...
Control and stopping of a diffusion process on an interval (1999)
Karatzas, Ioannis, Sudderth, William D.
Consider a process $X(\cdot) = {X(t), 0 \leq t < \infty}$ which takes values in the interval $I = (0, 1)$, satisfies a stochastic differential equation $$dX(t) = \beta(t)dt + \sigma(t)dW(t), X(0) = x...
A Barrier Option Of American Type (1998)
We obtain closed--form expressions for the prices and optimal hedging strategies of American put--options in the presence of an "up--and--out" barrier, both with and without constraints on the...
Stochastic and Control and Topics in Applied Probability. (1998)
We review the research, accomplished with the support of the above grant, in the broad areas of Stochastic Control and Applied Probability. Specific topics of interest include Singular Stochastic...
Stochastic Control and Topics in Applied Probability. (1998)
Research findings achieved under the auspices of the Army research grant on topics of Stochastic control under partial observations; Dynamic allocation and Multi-armed Bandit Problems; Deterministic...
Topics in Stochastic Analysis and Optimization of Systems (1998)
Cvitanic, Jaksa, Karatzas, Ioannis
Specific aims of our projects have been to study the following topics: (1) Backward Stochastic Differential Equations with reflection and connection with Dynkin games; (2) A deterministic approach to...
Backward stochastic differential equations with constraints on the gains-process (1998)
Cvitani{\'c}, Jak{\v{s}}a, Karatzas, Ioannis, Soner, H. Mete
We consider backward stochastic differential equations with convex constraints on the gains (or intensity-of-noise) process. Existence and uniqueness of a minimal solution are established in the case...
On Dynamic Measures of Risk (1998)
In the context of complete financial markets, we study dynamic measures for the risk associated with a given liability C at time t = T , of the form ae(x; C) := sup 2D inf ß(Delta)2A(x) E ` C Gamma...
On Dynamic Measures Of Risk (1998)
In the context of complete financial markets, we study dynamic measures for the risk associated with a given liability C at time t = T , of the form ae(x; C) := sup 2D inf (Delta)2A(x) E ` C Gamma X...
Hedging American contingent claims with constrained portfolios (1998)
The valuation theory for American Contingent Claims, due to Bensoussan (1984) and Karatzas (1988), is extended to deal with constraints on portfolio choice , including incomplete markets and...
Methods of Mathematical Finance (1998)
Karatzas, Ioannis, Shreve, Steven E.
Matemáticas financieras. Contenido: Modelos Brownianos para mercados financieros; Valuación de condiciones de demanda en el mercado total; Agentes simples, Consumo e inversiones; Equilibrio en el...
Methods of Mathematical Finance (1998)
Karatzas, Ioannis, Shreve, Steven E.
Matemáticas financieras. Contenido: Modelos Brownianos para mercados financieros; Valuación de condiciones de demanda en el mercado total; Agentes simples, Consumo e inversiones; Equilibrio en el...
Backward Stochastic Differential Equations with constraints on the gains-process (1997)
Ioannis Karatzas, H. Mete Soner
We consider Backward Stochastic Differential Equations with convex constraints on the gains (or intensity-of-noise) process. Existence and uniqueness of a minimal solution are established in the case...
Backward Stochastic Differential Equations with constraints on the gains-process (1997)
Ioannis Karatzas, H. Mete Soner
We consider Backward Stochastic Differential Equations with convex constraints on the gains (or intensity-of-noise) process. Existence and uniqueness of a minimal solution are established in the case...
On Portfolio Optimization Under "drawdown" Constraints (1996)
Jaksa Cvitanic, Ioannis Karatzas
We study the problem of portfolio optimization under the "drawdown constraint" that the wealth process never falls below a fixed fraction of its maximum-to-date, and one strives to maximize the...
Backward stochastic differential equations with reflection and Dynkin games (1996)
Cvitaniç, Jakša, Karatzas, Ioannis
We establish existence and uniqueness results for adapted solutions of backward stochastic differential equations (BSDE's) with two reflecting barriers, generalizing the work of El Karoui,...
A Strategic Market Game With Secured Lending (1995)
Ioannis Karatzas, Martin Shubik, William D. Sudderth
We study stationary Markov equilibria for strategic, competitive games, in a market-economy model with one non-durable commodity, fiat money, borrowing/lending through a central bank or a money...
Brownian Motion and Stochastic Calculus (1991)
Karatzas, Ioannis, Shreve, Steven E.
Libro de estadística matemática. Contenido: Martingalas, tiempo de frenado y filtraciones; Movimiento browniano; Integración estocástica; Movimiento browniano y ecuaciones diferenciales...
Brownian Motion and Stochastic Calculus (1991)
Karatzas, Ioannis, Shreve, Steven E.
Libro de estadística matemática. Contenido: Martingalas, tiempo de frenado y filtraciones; Movimiento browniano; Integración estocástica; Movimiento browniano y ecuaciones diferenciales...
Brownian motion and stochastic calculus / Ioannis Karatzas, Steven E. Shreve (1988)
Karatzas, Ioannis, Shreve, Steven E
Incluye bibliografía
A free boundary problem in stochastic optimal control /--Ioannis Karatzas. (1980)
Thesis (Ph. D.)--Columbia University, 1980.
Generalized Neyman-Pearson Lemma Via Convex Duality (1970)
We extend the classical Neyman-Pearson theory for testing composite hypotheses versus composite alternatives, using a convex duality approach as in Witting (1985). Results of Aubin & Ekeland (1984)...
Model Calibration in Mathematical Finance (1970)
Marco Avellaneda, Joshua Neal Newman, Jaksa Cvitanic, Cameron Connell, Darrell Due, Selim Esedoglu, ...
The subject of this thesis is the analysis of mathematical models used for pricing derivative securities and their calibration to market data. Our emphasis is on interest rate and credit derivatives...
A Leavable Bounded-Velocity Stochastic Control Problem (1970)
Ioannis Karatzas, Daniel Ocone
This paper studies bounded-velocity control of a Brownian motion when discretionary stopping, or `leaving', is allowed. The goal is to choose a control law and a stopping time in order to minimize...
A Stochastic Infinite-Horizon Economy with Secured Lending, or Unsecured Lending and Bankruptcy
Ioannis Karatzas, Martin Shubik, William D. Sudderth
Modeling problems for a monetary economy are discussed and some examples are presented in the context of an infinite-horizon economy with one or two types of traders, who use fiat money to buy a...
Inflationary Bias in a Simple Stochastic Economy
Ioannis Karatzas, Martin Shubik, William D. Sudderth, Geanakoplos, John
We construct explicit equilibria for strategic market games used to model an economy with fiat money, one nondurable commodity, countably many time- periods, and a continuum of agents. The total...
The Harmonic Fisher Equation and the Inflationary Bias of Real Uncertainty
Ioannis Karatzas, Martin Shubik, William D. Sudderth, John Geanakoplos
The classical Fisher equation asserts that in a nonstochastic economy, the inflation rate must equal the difference between the nominal and real interest rates. We extend this equation to a...
The implied liquidity premium for equities
Robert Fernholz, Ioannis Karatzas
Liquidity premium, Ranked market weights, Size effect, G12,
A Strategic Market Game with Active Bankruptcy
John Geanakoplos, Ioannis Karatzas, Martin Shubik, William D. Sudderth
We construct stationary Markov equilibria for an economy with fiat money, one non-durable commodity, countably-many time periods, and a continuum of agents. The total production of commodity remains...
The inflationary bias of real uncertainty and the harmonic Fisher equation
Ioannis Karatzas, Martin Shubik, William Sudderth, John Geanakoplos
We argue that real uncertainty itself causes long-run nominal inflation. Consider an infinite horizon cash-in-advance economy with a representative agent and real uncertainty, modeled by independent,...
Construction of Stationary Markov Equilibria in a Strategic Market Game
Ioannis Karatzas, Martin Shubik, William D. Sudderth
This paper studies stationary noncooperative equilibria in an economy with fiat money, one nondurable commodity, countably many time periods, no credit or futures market, and a measure space of...
Probabilistic aspects of finite-fuel stochastic control
The problem is that of following the Brownian path by a nondecreasing, bounded process in such a way as to minimize the expected cost over a finite horizon. Using purely probabilistic arguments, one...
Probabilistic aspects of finite-fuel stochastic control
The problem is that of following the Brownian path by a nondecreasing, bounded process in such a way as to minimize the expected cost over a finite horizon. Using purely probabilistic arguments, one...
Inflationary Bias in a Simple Stochastic Economy
Ioannis Karatzas, Martin Shubik, William D. Sudderth, John Geanakoplos
We construct explicit equilibria for strategic market games used to model an economy with fiat money, one nondurable commodity, countably many time- periods, and a continuum of agents. The total...
Relative arbitrage in volatility-stabilized markets
Robert Fernholz, Ioannis Karatzas
We provide simple, easy-to-test criteria for the existence of relative arbitrage in equity markets. These criteria postulate essentially that the excess growth rate of the market portfolio, a...
A Stochastic Overlapping Generations Economy with Inheritance
Ioannis Karatzas, Martin Shubik, William D. Sudderth
An overlapping generations model of an exchange economy is considered, with individuals having a finite expected life-span. Conditions concerning birth, death, inheritance and bequests are fully...
Information and the Existence of Stationary Markovian Equilibrium
Ioannis Karatzas, Martin Shubik, William D. Sudderth
We describe conditions for the existence of a stationary Markovian equilibrium when total production or total endowment is a random variable. Apart from regularity assumptions, there are two crucial...
A Strategic Market Game with Secured Lending
Ioannis Karatzas, Martin Shubik, William D. Sudderth
We study stationary Markov equilibria for strategic, competitive games, in a market-economy model with one non-durable commodity, fiat money, borrowing/lending through a central bank or a money...
Irreversible investment and industry equilibrium (*)
Ioannis Karatzas, Fridrik M. Baldursson
We establish the equivalence of competitive industry equilibrium with a central planner's decision problem under uncertainty, when investment is irreversible. The existence of industry equilibrium is...
Hedging American contingent claims with constrained portfolios
The valuation theory for American Contingent Claims, due to Bensoussan (1984) and Karatzas (1988), is extended to deal with constraints on portfolio choice, including incomplete markets and...
Ioannis Karatzas, Jaksa Cvitanic
In the context of complete financial markets, we study dynamic measures of the form \[ \rho(x;C):=\sup_{\nu\in\D} \inf_{\pi(\cdot)\in\A(x)}{\bf E}_\nu\left(\frac{C-X^{x, \pi}(T)}{S_0(T)}\right)^+, \]...
The Harmonic Fisher Equation and the Inflationary Bias of Real Uncertainty
John Geanakoplos, Ioannis Karatzas, Martin Shubik, William D. Sudderth
The classical Fisher equation asserts that in a nonstochastic economy, the inflation rate must equal the difference between the nominal and real interest rates. We extend this equation to a...
Diversity and relative arbitrage in equity markets
Robert Fernholz, Ioannis Karatzas, Constantinos Kardaras
An equity market is called “diverse” if no single stock is ever allowed to dominate the entire market in terms of relative capitalization. In the context of the standard Itô-process model...
The numéraire portfolio in semimartingale financial models
Ioannis Karatzas, Constantinos Kardaras
Numéraire portfolio, Semimartingale, Predictable characteristics, Free lunch, Supermartingale deflator, Log-utility, 60H05, 60H30, 91B28, G11,
The implied liquidity premium for equities
Robert Fernholz, Ioannis Karatzas
Liquidity premium, Ranked market weights, Size effect, G12,
A Strategic Market Game With Secured Lending
Ioannis Karatzas, Martin Shubik, William D. Sudderth
We study stationary Markov equilibria for strategic, competitive games, in a market-economy model with one non-durable commodity, fiat money, borrowing/lending through a central bank or a money...
Financial Control of a Competitive Economy without Randomness
Ioannis Karatzas, Martin Shubik, William D. Sudderth
The monetary and fiscal control of a simple economy without outside randomness is studied here from the micro-economic basis of a strategic market game. The government's bureaucracy is treated as a...