SOA QFI QFQuantitative Finance & Investment — Quantitative Finance

If $dS=\mu S\,dt+\sigma S\,dW$, then $d(\ln S)$ equals:

Derive the Black–Scholes partial differential equation for a European derivative $V(S,t)$ on a non-dividend stock, stating assumptions. Then explain why the real-world drift $\mu$ does not appear.

Explain the concept of asset-liability management (ALM) duration matching for a life insurer, and describe one limitation of simple duration matching that convexity matching addresses.