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REDUCING THE STATE SPACE FOR MULTIDIMENSIONAL PDE CASE

I=Inserting the equation and reordering it, we obtain:

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ffor ort -t rs - ))( ( )() F df- 8. (Te TsTes Fss- s= n-, = -, , 2)) ((( ) d)F FSTs t f (Tz TsTzT sr sF ssi n--sump - =condition - --i , ,i{ ¥7II FF ffor ort -t rs - )) ( OT(FCT ) F F8. (isTz ss ss n- - -- --, , - ,, )ohh( laItis) Fo tFg s.= -o . . ,We the2) continuo shydividendswhen timeconsider paid out incase are .)CatDlt between) dividends distributedcumulative=In the continuousthe usualto dividendsobtain with proceedinorder pose case aswe,dividendstheconstructing the butusual portfolio alsoconsidering :dst Std WedSt tStock DYNAMICS a rt: -. dividend8 ratethewhereSdt) St isd DHDynamicsDIVIDEND : = dbWe theintroduce ds DD old(Wwegain G S t SdDprocess t s att t r: = = = derivativesportfolio thethetheconstruct with and usualprocessusual proceedandgain asthe bondthe dynamicsrisk imposingremoving and :{ }DV TEV us t or-- .From formulaHo DFthe dpfdtt dinF withor :-: - .}IIII.{{ soft forde f 'sat-- :Sso¥. .. .. { } dt { }DV din)late VorUs areV t ort rus ort.= .

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..?÷÷I :S:L :::S :: ":we impose . .{ })DV dt(V dUs arofat t-= . II{ ¥ ft ' rfFs8)( os =t t -t -We )( dimpose Us ar PDEofat t r: =. )ElsFIT )st .=. ' ]" t (function therProposition Els ithas - whereThe )Flt - IIrepresentationpricing s e: =,dst d)Q by Crof dwtdynamics Std Stgivens t toare- : - --In martingalethedividendsdiscrete that dividendcontrast thewith inappropriatewe measureseefromdiffers dividendthat theofcase casemo(Proposition ) normalizedQthe martingale theneutral valuationRisk under gainmeasure:- ,process : ft ④GZA # martingalef d) DH is at -= ,callExample i lml¥)tl"dtFH""' "d "" )(Fft ) dcNlds) - N- daSte d VESt dywhereke-=, •. . , .=. THICURRENCY DERIVATIVESthe of thetorelated assets }riskrisk RISKSOFTYPES2productsQUAN

Dettagli
A.A. 2021-2022
111 pagine
SSD Scienze economiche e statistiche SECS-S/06 Metodi matematici dell'economia e delle scienze attuariali e finanziarie

I contenuti di questa pagina costituiscono rielaborazioni personali del Publisher bonadiamatilde di informazioni apprese con la frequenza delle lezioni di Matematica finanziaria 2 e studio autonomo di eventuali libri di riferimento in preparazione dell'esame finale o della tesi. Non devono intendersi come materiale ufficiale dell'università Politecnico di Milano o del prof Sgarra Carlo.