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In Section 6, we present a BSDEs approach to the valuation and hedging and derive examples of BSDEs for the gained value and the ex-dividend price.
We explore the valuation and hedging of discretely observed volatility derivatives using three different models for the price of the underlying asset: Geometric Brownian motion with constant volatility, a local volatility surface, and jump-diffusion.
The solution to the valuation and hedging problem described by (16) and (18) can be obtained in terms of standard BSDEs under (Pin mathcal {P}_{[underline {a},overline {a}]}).
More recently, Crépey (2015a, b), Dumitrescu et al. (2017) and Bichuch et al. (2018) used BSDEs with jumps to solve the valuation and hedging problems for derivative contracts exposed to the counterparty credit risk.
Indeed one would need, by the preceding valuation and hedging Theorems 1 and 2, first to identify a candidate worst-case drift parameter (bar {theta }) (and then possibly a worst-case volatility) satisfying (36).
However, for incomplete markets (i.e., for dvaluation and hedging, that are less expensive than superreplication.
Similar(45)
Beyond this, (15) will also be used to prove wellposedness of a 2BSDE whose solution will describe the robust good-deal valuation bound and hedging strategy (see Theorems 1 and 2, respectively).
The approach to valuation and hedging-to-acceptability that shows in Eqs.
Goldman, by contrast, tends to be more systematically focused on managing its risk, and because it is more active in modeling, trading and hedging its portfolios, its valuation measures would be more strongly grounded in market pricing.
His focus on trading a diverse basket of currencies and hedging contracts looked lackluster compared with the soaring valuations of technology stocks.
Instead, we will rely on 2BSDE theory to provide in Section "Good-deal hedging and valuation under combined uncertainty", under combined uncertainty about drifts and volatilities, a differential characterization of (robust) good-deal bounds and hedging strategies, after suitably defining the latter in such a typically non-dominated setup.
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