Online Strategy For Financial Decision-making Problems And Its Competitive Analysis

The online algorithm developed in theoretical computer science makes no statis-tical assumption about the future inputs and makes decision only based on availabledata. These properties provide new ideas and methods for the research of many financialdecision-making problems whose decision strategies preserve online property. This thesisfirst states the background and significance of the research about equipment asset leas-ing, single risk asset investment and various risk assets investment; and presents a reviewabout the origin and development of decision-making theory and the related research'sstatus. Based on that, this thesis, considering actual situation, further applies the tra-ditional competitive analysis to study the online leasing strategy and risk strategies ofthe equipment asset. This thesis explores the online investment strategy of single riskasset, and provides the conservative strategy that bases on risk aversion and the riskstrategy that bases on forecast, respectively. Based on linear learning function, this the-sis presents online investment strategy of various risk assets and provides its competitiveperformance analysis. This thesis applies the weak aggregating algorithm to online in-vestment of various risk assets and obtains the specific strategies. There exists diferencebetween the research methods of online leasing of equipment asset, online investment ofsingle risk asset and online investment of various risk assets. However, the relationshipis also obvious since their inputs are both obtained in online manner, their decisions areboth decided according to historical data and they both need to choose a benchmark toevaluate the competitive performance of the presented online strategies. The online leas-ing of equipment asset is one of the simplest and basic risk decision-making problems. Itsresearch methods can be generalized to online investment of single risk asset and variousrisk assets, and online investment of single risk asset is a special case of online investmentof various risk assets. The main creative results of the research are as follows:1. Study the online leasing problems that are afected by the change of supply-demand's relationship, the free market's flexibility and the discontinuous usage and con-struct the corresponding online leasing models and obtain their competitive performanceanalysis by using competitive analysis.The purchase cost and rent cost of an equipment usually change with the demand; inthe same time, as the development of technology, the brands of equipment are various; andthe interest rate will afect the online strategy of discontinuous use of equipment. Basedon these situations, this thesis studies the online leasing strategy with discrete change of equipment's price and its competitive performance, explores the online randomizedselection strategy of the depreciable equipment with many obtaining's methods, andprovides the two period online leasing strategy that is afected by interest rate, and itscompetitive performance analysis.2. As the large scale equipment is depreciable and the secondary market exists,this thesis constructs the online leasing model of depreciable equipment and obtains itsdeterministic strategy, randomized strategy and risk strategies that base on forecast.Most of previous research on equipment leasing problems base on that the equipmentcan be used for ever once it is bought, and did not provide a system study on onlineleasing strategy of depreciable equipment. This thesis on the basis of the model of onlineleasing of depreciable equipment, first provides its deterministic strategy and randomizedstrategy; then gives its risk strategies based on certain forecast and probability forecast,respectively; Lastly, this thesis apply the risk strategy that obtained under certain forecastto two period online replacement problem. The results show that the introduction ofdepreciation has enabled the competitive performances of both deterministic strategyand randomized strategy get improved, and the introduction of interest rate made thethe competitive ratio of deterministic strategy get decreased while that of randomized getincreased; the optimal competitive ratio of risk strategy is decreased, and the extent towhich is related to risk tolerance; in the same time, the results also show the risk strategyunder probability forecast has generalized the one under certain forecast.3. This thesis studies the online investment of single risk asset under the situationsthat the return rate are linear-growth and log-growth; constructs the risk-reward modelwith period forecast for online investment of one risk asset. This paper then obtains theconservative strategy and risk strategy for online investment of single risk asset.The fluctuation of real return rate is various. Based on the risk aversion, this thesispresents the conservative strategies for the return rates that are linear-growth and log-growth, respectively. Numerical analysis shows the conservative strategy that bases onrisk aversion is more suitable for the stable return rate series. The existed risk strategyis based on the forecast of one point of the return rate series; this thesis based on theperiod forecast provides risk strategy for online investment of single risk asset and itscompetitive performance. The numerical analysis results show the average improvementof optimal restricted competitive ratio is closely related to the investor's risk toleranceand is proportional to the risk tolerance.4. This paper studies the online investment of various risk assets and constructs theonline portfolio selection strategy that bases on linear learning function, and constructsonline investment model for various risk assets based on the weak aggregating algorithmand obtains online invest strategy that has better competitive performance.Based on the on-line learning of linear function, this thesis presents on-line invest- ment strategy for various risk assets, where the linear coefcient is the middle of aninterval. And the interval is related to risk assets' returns. Using the relative entropy asthe distance function of two portfolios, this paper proves that the provided on-line portfo-lio is universal. The linear factor can be any point of the interval and a class of universalportfolio is obtained. This thesis explores the application of weak aggregating algorithmto online investment of various risk assets. First, apply it to the experts' strategies thatinvest on single risk asset and obtain the portfolio selection algorithm WAAS. Considerthe definition of universal portfolio is based on BCRP, so this thesis further applies theweak aggregating algorithm to CRP, and obtains the portfolio selection algorithm WAAC.Theoretical and numerical results illustrate the return of WAAS strategy is as good asthat of the best risk asset, and the return of the WAAC is as good as that of the BCRP.