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3761Choosing a Numeraire for a Benchmark-Relative Performance FeeA fee depends on how a fund performs relative to a benchmark index. Why might the benchmark itself be a sensible numeraire candidate?随机过程中等essay未尝试面试订阅3762Why a Forward Measure Is About Convenience, Not a Different PriceA candidate worries that switching to a forward measure must change the answer because the probability law changes. What is the correct reply?随机过程中等essay未尝试面试订阅3763Why Asset Numeraires Help with Share-Settled DerivativesWhy are asset numeraires especially natural when a derivative settles in units of the underlying rather than in cash?随机过程中等essay未尝试面试订阅3764How Settlement Timing Guides the Numeraire ChoiceIf you know nothing else about a payoff except that it settles at a single future date, what numeraire heuristic is often the best starting point?随机过程中等essay未尝试面试订阅3765Why Annuity, Bond, and Money-Market Numeraires Can All Be Right in Different RepresentationsHow can annuity, bond, and money-market numeraires all be valid choices for related rates problems without creating contradiction?随机过程中等essay未尝试面试订阅3766Half-Life of a Moderately Mean-Reverting SpreadAn OU deviation decays in mean like e (-kappa t) with kappa = 0.35. What is its half-life?随机过程中等derivation未尝试面试订阅3771Speed Implied by a 40% Gap After One YearIn an OU model, the expected deviation from the long-run mean shrinks by a factor 0.4 over 1 years. What kappa does this imply?随机过程中等derivation未尝试面试订阅3773Speed Implied by a 60% Gap After Half a YearIn an OU model, the expected deviation from the long-run mean shrinks by a factor 0.6 over 0.5 years. What kappa does this imply?随机过程中等derivation未尝试面试订阅3776Diffusion Strength from a Stationary Variance TargetAn OU process has mean-reversion speed kappa = 0.8 and stationary variance 0.5. What diffusion coefficient sigma is implied?随机过程中等derivation未尝试面试订阅3781Long-Run Mean from a One-Year Expected LevelAn OU process starts at X 0 = 8 and has mean-reversion speed kappa = 0.6. If E[X 1] = 5.6, what long-run mean theta is implied?随机过程中等derivation未尝试面试订阅3782Long-Run Mean from a Half-Year Reversion TargetAn OU process starts at X 0 = 2.5 and has mean-reversion speed kappa = 1.2. If the expected value at t = 0.5 is 1.4, what long-run mean theta is implied?随机过程中等derivation未尝试面试订阅3784Long-Run Mean from a Mid-Horizon ForecastAn OU process starts at X 0 = 1.5 and has mean-reversion speed kappa = 0.9. If E[X 1.5] = 2.1, what long-run mean theta is implied?随机过程中等derivation未尝试面试订阅3786Why OU Is Mean-Reverting but Brownian Motion Is NotWhat is the structural reason an OU process is mean-reverting while plain Brownian motion is not?随机过程中等essay未尝试面试订阅3787Why Half-Life Is a Better Summary Than One-Step DriftWhy do practitioners often summarize an OU process by half-life instead of by quoting the raw drift coefficient alone?随机过程中等essay未尝试面试订阅3788Why Stationary Variance Balances Sigma Against KappaWhy does the OU stationary variance depend on both sigma and kappa instead of on the diffusion coefficient alone?随机过程中等essay未尝试面试订阅3789Why a Large Kappa Can Hide a Large SigmaHow can an OU process have a large diffusion coefficient and still look tightly clustered around its mean?随机过程中等essay未尝试面试订阅3790Why OU Is Often a Better Spread Model Than a Random WalkWhy is OU often a more plausible model than a random walk for a spread that traders believe should revert?随机过程中等essay未尝试面试订阅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