Portfolio Management with Drawdown Constraint: An Analysis of Optimal Investment

2017 ◽  
Author(s):  
Maxime Bonelli ◽  
Mireille Bossy
Keyword(s):  
Portfolio Management ◽  
Optimal Investment ◽  
Drawdown Constraint

Reaching goals by a deadline: digital options and continuous-time active portfolio management

1999 ◽  
Vol 31 (02) ◽  
pp. 551-577 ◽  
Author(s):  
Sid Browne
Keyword(s):  
Portfolio Management ◽  
Optimal Policy ◽  
Optimal Strategy ◽  
Optimal Growth ◽  
Optimal Investment ◽  
External Source ◽  
Strike Price ◽  
Terminal Time ◽  
Active Portfolio Management ◽  
Digital Options

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 + 1 investment opportunities: n 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.

Reaching goals by a deadline: digital options and continuous-time active portfolio management

1999 ◽  
Vol 31 (2) ◽  
pp. 551-577 ◽  
Author(s):  
Sid Browne
Keyword(s):  
Portfolio Management ◽  
Optimal Policy ◽  
Optimal Strategy ◽  
Optimal Growth ◽  
Optimal Investment ◽  
External Source ◽  
Strike Price ◽  
Terminal Time ◽  
Active Portfolio Management ◽  
Digital Options

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 + 1 investment opportunities: n 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.

Advantages and Disadvantages of Contemporary Methods for Evaluation of Efficiency of Investment in Intellectual Property Items

10.12737/6729 ◽  
2014 ◽  
Vol 2 (6) ◽  
pp. 15-22
Author(s):  
Левкина ◽  
Nataliya Levkina
Keyword(s):  
Intellectual Property ◽  
Portfolio Management ◽  
Optimal Investment ◽  
Efficiency Evaluation ◽  
Financial Assets ◽  
Investment Portfolio ◽  
Investment Projects ◽  
Advantages And Disadvantages ◽  
Traditional Classification ◽  
Rational Combination

Contemporary methods of investment projects’ efficiency evaluation are based on such fundamental finance theories as J. Williams’ theory of discounted cash flows, investment portfolio management, pricing model for financial assets and the theory of options. All these theories were originally intended for analysis of investment in securities. This paper provides an overview of contemporary methods for evaluation of efficiency of investment projects connected with acquisition, development and use of intellectual property items in the frames of traditional classification, according to which they are commonly divided into three groups: financial, probabilistic and qualitative. As all financial, probabilistic and qualitative methods for evaluation of efficiency of investment in intellectual property items have their advantages and disadvantages it is recommended to use these methods’ rational combination in order to choose the optimal investment variant.

scholarly journals On Application of Matlab on Efficient Portfolio Management for a Pension Plan in the Presence of Uneven Distributions of Accumulated Wealth

2020 ◽  
pp. 43-54
Author(s):  
Obasi, Emmanuela C. M. ◽  
Akpanibah, Edikan E.
Keyword(s):  
Portfolio Management ◽  
Efficient Frontier ◽  
Pension Plan ◽  
Optimal Investment ◽  
Risky Assets ◽  
Investment Plan ◽  
Stochastic Optimal Control Problem ◽  
Plan Member ◽  
Time Inconsistent ◽  
Mean Variance

In this paper, we solved the problem encountered by a pension plan member whose portfolio is made up of one risk free asset and three risky assets for the optimal investment plan with return clause and uneven distributions of the remaining accumulated wealth. Using mean variance utility function as our objective function, we formulate our problem as a continuous-time mean–variance stochastic optimal control problem. Next, we used the variational inequalities methods to transform our problem into Markovian time inconsistent stochastic control, to determine the optimal investment plan and the efficient frontier of the plan member. Using mat lab software, we obtain numerical simulations of the optimal investment plan with respect to time and compare our results with an existing result.

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