一个风险敏感最优控制问题的随机最大值原理及在投资选择中的应用(英文)-豆柴文库

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一个风险敏感最优控制问题的随机最大值原理及在投资选择中的应用(英文)
TheRandomMaximumPrincipleinRisk-SensitiveOptimalControlProblemsandItsApplicationinInvestmentDecision-Making
I.Introduction
Optimalcontroltheoryprovidesapowerfulframeworkforanalyzingandsolvingvariouscontrolproblemsinengineering,economics,andfinance.Inmanypracticalapplications,onecrucialconsiderationishowtoincorporaterisksensitivityintothecontroloptimizationproblem.Thiscanbeachievedbyadoptingriskmeasuresthatcapturetheuncertaintyandvolatilityassociatedwiththesystembeingcontrolled.Inthispaper,wewillexploretherandommaximumprinciple,afundamentalprincipleinrisk-sensitiveoptimalcontrol,anditsapplicationininvestmentdecision-making.
II.TheRandomMaximumPrinciple
Therandommaximumprincipleisanextensionoftheclassicalmaximumprinciple,originallydevelopedbyPontryagin,fordeterministicoptimalcontrolproblems.Itprovidesnecessaryconditionsfortheexistenceofoptimalcontrolsinrisk-sensitivecontrolsettings,wheretheobjectiveistominimizearisk-sensitiveperformancecriterion.
Therisk-sensitiveperformancecriterionisusuallydefinedintermsofacostfunctionalthatincorporatesariskmeasure.Ariskmeasurequantifiesthelevelofuncertaintyorriskassociatedwiththecontrolsystem.Commonlyusedriskmeasuresincludeexpectedutility,conditionalvalue-at-risk,andentropy-basedmeasures.Therandommaximumprincipleoffersasystematicapproachtoderiveoptimalcontrolsthatachievetheminimumrisk-sensitivecost.
III.ApplicationinInvestmentDecision-Making
Investmentdecision-makingisaclassicexampleofaproblemthatrequiresrisk-sensitiveoptimalcontrol.Investorsoftenfaceuncertaintiesandrisksassociatedwithmarketvolatility,interestrates,andeconomicconditions.Thegoalistodeterminetheoptimalallocationofresourcestodifferentinvestmentoptionswhileconsideringriskpreferencesandmaximizingreturns.
Byincorporatingriskmeasuresintotheinvestmentdecision-makingprocess,therandommaximumprinciplecanhelpinvestorsmakeinformedandprudentinvestmentchoices.Itenablesinvestorstoquantifyandmitigaterisksassociatedwithdifferentinvestmentalternativ