Equity valuation under stock dilution and buy-back (Q449281)

A model which consists of:NEWLINENEWLINE1) a finite set of stochastic tradables \(S(t)\),NEWLINENEWLINE2) a finite set of dynamic factors \(A(t)\),NEWLINENEWLINE3) a money market with the (short) rate \(r(t, A(t))\),NEWLINENEWLINEand assumed to obey SDE dynamics NEWLINE\[NEWLINE dS(t)= S(t)(a_s(t, A(t))-\mathbb{D}(t, A(t)))+S(t)\sigma_s(t, A(t))dB(t) NEWLINE\]NEWLINE NEWLINE\[NEWLINE dA(t)= b(t, A(t))dt+c(t, A(t))dB(t) NEWLINE\]NEWLINE is considered. The model is extended to account for a possibility of stock dilution and buy-back. The associated pricing PDE system and the hedging formula are derived. Both, neutral and indifference pricing methodologies are considered, and results of different levels of complexity are provided.