Advances in Quantitative Analysis of Finance and Accounting by Cheng-Few Lee

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By Cheng-Few Lee

Advances in Quantitative research of Finance and Accounting is an annual ebook designed to disseminate contemporary advancements within the quantitative research of finance and accounting. The e-book is a discussion board for statistical and quantitative analyses of matters in finance and accounting in addition to purposes of quantitative the right way to difficulties in monetary administration, monetary accounting, and company administration. Its goal is to advertise interplay among educational study in finance and accounting with utilized examine within the monetary neighborhood and the accounting career. The chapters during this quantity conceal quite a lot of urgent issues together with safeguard research and mutual fund administration, choice pricing thought and alertness, rate of interest unfold, and electrical energy pricing.

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Example text

If f d ( dd ) = 0, then f d (γ ) = 0 has at most one more solution in addition to uu . Again the cost function C( uu , d ) = C( d ) is linear in any interval not containing uu , dd , or any of the γ ’s. So the minimum must be achieved at one of these points. Suppose it is achieved at d = uu . Then the one-period claim {( uu , Buu /R), ( d , bd ( d )/R)} = {( uu , Buu /R), ( uu , Buu /R)} is in Case 2 of Remark 1 so that by Theorem 4 the unique replicating portfolio ( uu , Buu /R 2 ) is the least cost superreplicating portfolio.

This is type (II)(a) of Theorem 7. 3. We consider next the case f d ( uu ) > 0 and R(1 + λ) > u(1 − µ) so that f d is strictly decreasing. Then ad > 0 for all d = uu , and au > 0 for d > uu , and au < 0 for d < uu and au ( uu ) = ad ( uu ) = 0. Then f d (γ ) = 0 has exactly one solution γ which is greater than uu . Again we see from Remark 1 that the cost function C( uu , d ) = C( d ) is linear in any interval not containing uu , dd , or γ . So the minimum must be achieved at one of these points.

Thus, if f d ( uu ) < 0,  < 0 if d < δ, au = 0 if d = δ,  > 0 if δ < d ≤ uu . au = We now consider four different cases. 1. Suppose first that f d ( uu ) < 0. Then ad > 0 for all d , au > 0 for d > δ, and au (δ) = 0 and au < 0 for d < δ. Also f d (γ ) = 0 has at most three solutions. As the function bd ( d ) is linear in any interval not containing uu , dd , or any of the γ ’s, we see from Remark 1 that the cost function C( uu , d ) = C( d ) is linear in any interval not containing δ, uu , dd , or any of the γ ’s.

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