These notes are based on a series of four lectures given at a symposium on stochastic processes, held in May 2000 at CIMAT, Guanajuato, Mexico. The lectures provide a concise introduction to some stochastic control problems in mathematical nance. More specically,
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311
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Portfolio Selection
– Markowitz
- 1952
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180
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Random perturbations of dynamical systems
– Freidlin, Wentzell
- 1984
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121
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Numerical Methods for Stochastic Control Problems in Continuous Time
– Kushner, Dupuis
- 1992
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111
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Optimal Control and Viscosity Solutions of Hamilton-Jacobi-Bellman Equations
– Bardi, Capuzzo-Dolcetta
- 1997
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71
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Risk Sensitive Optimal Control
– Whittle
- 1990
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44
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Dynamic Programming and Optimal Control,” vols
– Bertsekas
- 1995
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44
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Strategic asset allocation
– Brennan, Schwartz, et al.
- 1997
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41
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Approximation schemes for viscosity solutions of Hamilton-Jacobi equations
– Souganidis
- 1985
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41
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The Mathematics of Financial Derivatives
– Wilmott, Howison, et al.
- 1995
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35
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Optimal Stochastic Linear Systems with Exponential Performance Criteria and Their Relation to Deterministic Games
– Jacobson
- 1973
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34
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Portfolio Selection with Transactions Costs
– Davis, Norman
- 1990
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32
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Nonlinear elliptic and parabolic equations of the second order
– Krylov
- 1987
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22
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Differential games and representation formulas for solutions of Hamilton-Jacobi-Issacs equations
– Evans, Souganidis
- 1984
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22
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Introduction to Mathematical Finance: Discrete Time Models
– Pliska
- 1999
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19
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Optimal Control: Basics and Beyond
– Whittle
- 1996
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12
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Derivatives in Financial Markets with stochastic Volatility
– Fouque, Papanicoloau, et al.
- 2000
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11
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Controlled Di#usion Processes
– Krylov
- 1980
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10
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Bellman equations of risk-sensitive control
– Nagai
- 1996
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8
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Risk-sensitive control of markov processes in countable state space
– Hern'andez-Hern'andez, Marcus
- 1996
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7
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unknown title
– Lions
- 1983
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6
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Dynamic asset pricing theory, 2nd Ed
– Due
- 1996
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6
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Dierential games
– Isaacs
- 1965
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5
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Risk-sensitive control on an in time horizon
– Fleming, McEneaney
- 1995
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5
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Uniqueness of viscosity solutions of nonstationary HJB equations under some prior conditions (with applications
– McEneaney
- 1995
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4
|
The risk-sensitive index and the H 2 and H1 norms for nonlinear systems
– Fleming, James
- 1995
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3
|
Risk sensitive dynamic asset management
– Bielecki, Pliska
- 1999
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3
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A users guide to viscosity solutions
– Crandall, Ishii, et al.
- 1992
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2
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Some results on risk-sensitive control with full observation
– Bensoussan, Frehse, et al.
- 1998
|
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2
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Existence of value in dierential games
– Elliott, Kalton
- 1972
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2
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Drift and volatility estimation in discrete time
– Elliott, Hunter, et al.
- 1998
|
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2
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Risk sensitive control of state machines on an in horizon I
– Fleming, Hernandez-Hernandez
- 1997
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2
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Risk sensitive control and dierential games
– Fleming, McEneaney
- 1992
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2
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Deterministc and Stochastic Control
– FLEMING, RISHEL
- 1975
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2
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Optimal long term growth rate of expected utility ofwealth
– Fleming
- 1999
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2
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Asymptotic analysis of nonlinear risk-sensitive control and differential games
– James
- 1992
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2
|
Bellman-Isaacs equations of ergodic type related to risksensitive control and their singular limits, Asymptotic Anal
– Kaise, Nagai
- 1998
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2
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Risk sensitive dynamic asset management with partial information, to appear in G. Kallianpur 75th anniversary volume
– Nagai
|
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2
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Optimal portfolio management with partial observations and power utility function
– Rishel
- 1999
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1
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Risk sensitive control of state Markov chains in discrete time with applications to portfolio management
– Bielecki, Hernandez-Hernandez, et al.
- 1999
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1
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Filtering derivative security evaluations from market prices
– Elliott, Madan, et al.
- 1995
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1
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The convergence problem for dierential games II, in M. Dresher et al (eds
– Fleming
- 1964
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1
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Controlled Markov processes and mathematical in Nonlinear Analysis, Dierential Equations and Control
– Fleming
- 1999
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1
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Risk sensitive control and an optimal investment model
– Fleming, Sheu
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1
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A Stochastic optimal control approach to international and foreign debt, CES ifo Working Paper No
– Fleming, Stein
- 1999
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1
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A robust control framework for option pricing
– McEneaney
- 1997
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1
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Principles for modelling markets
– Platen, Rebolledo
- 1996
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