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|a (JST)1428122
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|a DE-627
|b ger
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|a eng
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|a 90A09
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1 |
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|a Browne, Sid
|e verfasserin
|4 aut
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| 245 |
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|a Reaching Goals by a Deadline: Digital Options and Continuous-Time Active Portfolio Management
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|c 1999
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|a Text
|b txt
|2 rdacontent
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|a Computermedien
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|a Online-Ressource
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|a We study a variety of optimal investment problems for objectives related to attaining goals by a fixed terminal time. We start by finding the policy that maximizes the probability of reaching a given wealth level by a given fixed terminal time, for the case where an investor can allocate his wealth at any time between n investment opportunities: n+1 risky stocks, as well as a risk-free asset that has a positive return. This generalizes results recently obtained by Kulldorff and Heath for the case of a single investment opportunity. We then use this to solve related problems for cases where the investor has an external source of income, and where the investor is interested solely in beating the return of a given stochastic benchmark, as is sometimes the case in institutional money management. One of the benchmarks we consider for this last problem is that of the return of the optimal growth policy, for which the resulting controlled process is a supermartingale. Nevertheless, we still find an optimal strategy. For the general case, we provide a thorough analysis of the optimal strategy, and obtain new insights into the behavior of the optimal policy. For one special case, namely that of a single stock with constant coefficients, the optimal policy is independent of the underlying drift. We explain this by exhibiting a correspondence between the probability maximizing results and the pricing and hedging of a particular derivative security, known as a digital or binary option. In fact, we show that for this case, the optimal policy to maximize the probability of reaching a given value of wealth by a predetermined time is equivalent to simply buying a European digital option with a particular strike price and payoff. A similar result holds for the general case, but with the stock replaced by a particular (index) portfolio, namely the optimal growth or log-optimal portfolio.
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|a Copyright 1999 Applied Probability Trust
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| 650 |
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4 |
|a Optimal gambling
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| 650 |
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4 |
|a Stochastic control
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| 650 |
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4 |
|a Portfolio theory
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| 650 |
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4 |
|a Martingales
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| 650 |
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4 |
|a Option pricing
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| 650 |
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4 |
|a Hedging strategies
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| 650 |
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4 |
|a Digital options
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| 650 |
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4 |
|a Economics
|x Economic disciplines
|x Financial economics
|x Finance
|x Financial investments
|x Investors
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| 650 |
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4 |
|a Behavioral sciences
|x Psychology
|x Cognitive psychology
|x Cognitive processes
|x Decision making
|x Optimal policy
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| 650 |
|
4 |
|a Business
|x Business economics
|x Commercial production
|x Production resources
|x Resource management
|x Time management
|x Deadlines
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| 650 |
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4 |
|a Economics
|x Economic policy
|x Investment policy
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| 650 |
|
4 |
|a Economics
|x Economic disciplines
|x Socioeconomics
|x Wealth
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| 650 |
|
4 |
|a Economics
|x Economic disciplines
|x Financial economics
|x Finance
|x Financial management
|x Portfolio management
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| 650 |
|
4 |
|a Mathematics
|x Pure mathematics
|x Calculus
|x Differential calculus
|x Differential equations
|x Ordinary differential equations
|x Constant coefficients
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| 650 |
|
4 |
|a Economics
|x Economic disciplines
|x Financial economics
|x Finance
|x Financial instruments
|x Financial securities
|x Dilutive securities
|x Stock options
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| 650 |
|
4 |
|a Economics
|x Economic disciplines
|x Financial economics
|x Finance
|x Financial investments
|x Financial portfolios
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| 650 |
|
4 |
|a Mathematics
|x Pure mathematics
|x Probability theory
|x Random variables
|x Stochastic processes
|x Martingales
|x General Applied Probability
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| 655 |
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4 |
|a research-article
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| 773 |
0 |
8 |
|i Enthalten in
|t Advances in Applied Probability
|d Applied Probability Trust
|g 31(1999), 2, Seite 551-577
|w (DE-627)269247009
|w (DE-600)1474602-5
|x 00018678
|7 nnns
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| 773 |
1 |
8 |
|g volume:31
|g year:1999
|g number:2
|g pages:551-577
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| 856 |
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|u https://www.jstor.org/stable/1428122
|3 Volltext
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|d 31
|j 1999
|e 2
|h 551-577
|