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3791Discounted Terminal Payoff and the -ru TermA PDE contains u t + L u - r u = 0 with terminal condition u(T,x)=g(x). What discounting structure should appear in the Feynman-Kac expectation, and why?随机过程中等essay未尝试面试订阅3792Running Reward and the Source-Term SignIf the expectation contains an accumulated running reward integral t T f(s,X s) ds added to the terminal payoff, what sign should f have inside the PDE representation?随机过程中等essay未尝试面试订阅3793Terminal Condition as the Future Payoff RuleWhy should the terminal condition u(T,x)=g(x) be read as the payoff rule at the horizon rather than as an arbitrary boundary artifact?随机过程中等essay未尝试面试订阅3794Absorbing Boundary as Path TerminationHow should an absorbing boundary condition be interpreted inside a Feynman-Kac representation?随机过程中等essay未尝试面试订阅3795Generator Terms as Local Drift and DiffusionIn a Feynman-Kac PDE, what is the role of the operator L built from first and second spatial derivatives?随机过程中等essay未尝试面试订阅3796From Expectation to PDE Without Memorizing the FormulaIf you forget the exact Feynman-Kac formula, what conceptual ingredients let you rebuild the corresponding PDE from a discounted expectation anyway?随机过程中等essay未尝试面试订阅3797Why a Positive Running Cost Creates a Negative Economic EffectA model writes a positive running cost c inside the expectation as something being subtracted over time. How should that appear in the PDE, conceptually?随机过程中等essay未尝试面试订阅3798Why Time Runs Backward in Pricing PDEsWhy does the PDE associated with a terminal payoff usually run backward from T to t instead of forward from now to maturity?随机过程中等essay未尝试面试订阅3799Why Boundary Conditions Matter Even When the Terminal Payoff Is KnownIf the terminal payoff is already specified, why do boundary conditions still matter in many Feynman-Kac problems?随机过程中等essay未尝试面试订阅3800Discounting as State-Dependent KillingWhy is the term -r(x,t)u often interpreted as a state-dependent killing rate in the Feynman-Kac picture?随机过程中等essay未尝试面试订阅3801Mapping a PDE with No Source and No DiscountIf the PDE has u t + L u = 0 with only a terminal condition, what is the corresponding expectation structure?随机过程中等essay未尝试面试订阅3802Mapping a PDE with Discount and Source TogetherIf a PDE contains both -r u and +f, what two separate pathwise ingredients should appear in the expectation representation?随机过程中等essay未尝试面试订阅3803Why the Diffusion Coefficient Touches the Second DerivativeWhy does the diffusion strength of the state process appear in front of the second spatial derivative in the PDE?随机过程中等essay未尝试面试订阅3804Why Drift Touches the First DerivativeWhy does the drift coefficient show up next to the first spatial derivative in the PDE?随机过程中等essay未尝试面试订阅3805Reading a Running Penalty from the PDEA backward PDE includes a negative source term. What economic story should you suspect in the underlying expectation?随机过程中等essay未尝试面试订阅3806Why Feynman-Kac Is a Bridge, Not Two Separate FactsWhy is it better to think of Feynman-Kac as a bridge between probabilistic expectations and PDEs rather than as two separate formulas to memorize?随机过程中等essay未尝试面试订阅3807Barrier Knock-Out as Boundary DataFor a knock-out style problem, why does the boundary condition typically encode zero continuation value after a hit?随机过程中等essay未尝试面试订阅3808Why a Source-Free PDE Still Carries Rich EconomicsIf a PDE has no source term at all, why is it still not 'empty' from an economic point of view?随机过程中等essay未尝试面试订阅3809Expectation with a Stopping Time Instead of Fixed TIf an expectation stops at a hitting time rather than at a fixed maturity, what change should you expect on the PDE side?随机过程中等essay未尝试面试订阅3810Why State Dependence in r or f Matters PathwiseWhat changes in the expectation picture when discount or running reward depends on the current state X s rather than on time alone?随机过程中等essay未尝试面试订阅