Directional derivative

2. The PZK Co will take out a forward exchange contract, the foreign exchange contract is define as an agreement of two sides to determine in a specified amount of currency exchange on a valid date. The advantages of PZK Co use forward contracts are that, the company can hedge their imports by locking the currency rate, to avoid the unfavourable exchange rate and fluctuations thus the company can make use of the forward contract to ensure the exchange rate is fixed at the deal day. Moreover, the…

and differentiation. It says that a function when differentiated, can be brought back by integrating (anti-derivative) or a function when integrated, can be brought back by differentiation. First theorem: Let f be a function that is integrable on [a,x] for each x in [a,b], then let c be such that a≤c≤b and define a new function A as follows, A(x)=∫_c^x▒f(x)dt, if a≤x≤b. Then the derivative A’(x) exists at each point x in the open interval (a,b) where f is continuous, and for such x, A^'…

When Should Your Company Issue Restricted Equity vs. Options and When is 83(b) Applicable to Recipients’ Equity? Since forming your entity, you issued restricted equity to recipients regularly, but you closed a recent funding round. And this week your attorney says you should no longer issue restricted equity, and instead, you need an option plan and to issue options. What is he talking about and why is it necessary? Plus, when should the recipients file an 83(b) election? Restricted Equity vs…

As business becomes more globalized and trade continues to expand internationally, companies need to understand and reduce the risk associated with international business. Though there are many risks faced by companies when operating internationally, including political, financial, and cultural, this paper will specifically discuss the financial risk associated with exchange rates and how companies mitigate this risk through currency hedging. Foreign Exchange Risks Foreign exchange risk is “the…

a quasi-uniform family {Qh} of meshes on Ω into quadrilaterals. Then a necessary condition for ∥u − uh∥ Ls(Ω) = O(hp+1) is for uh to be Wp+1 s smooth. In particular, for ∥u − uh∥ L∞(Ω) = O(hp+1) a necessary condition is that all the kth partial derivatives at xi ∈ T satisfy (41) @(u − uh)(xi) = O(hp+1−k); || = k; 0 ≤ k ≤ p: In other words, we have a simultaneous approximation result. Here all smoothness refers to interior smoothness and {xi} is any collection of points, one from each element.…

According to Hull, J (Options, Futures and other derivatives: page 7); Options are traded both on exchanges and in the over-the-counter markets. There are two types of option; there is a Call Option and Put Options. The Call Option gives the owner the ability to trade a specified amount of products at a fixed price; and the put option is option which gives the owner the right to sell the underlying asset by a certain date for a certain price. And there are styles of options: American Options and…

If R and r is the Circumradius and Inradius of a non-degenerate triangle then due to Euler we have an Inequality stated as and the equality holds when the triangle is equilateral. This ubiquitous inequality occurs in the literature in many different equivalent forms [4] and also Many other different simple approaches for proving this inequality are known. (some of them can be found in [2], [3], [5], [17], and [18] ). In this article we present a proof for this Inequality based on two basic…

changing like area, distance, or volume. In order to solve related rates problems you need to be able to recall or have access to basic geometry formulas like circle, cone, cylinder, rectangle, triangle and square. Also you need to know how to take a derivative, and being able to understand what you are given and what you need to find in a related rates problem. The first thing you should do in a related rates problem is read the problem to get an understanding…

requires solid sample state analysis, which is not performed in this study. Therefore, trying to attempt a double derivative of the absorption by plotting the points and found a polynomial (third degree) trend line, performed a single and double derivative to determine the changes slopes. The first derivative determines speed of slope change: onset wavelength of peak and theory: second derivative finds acceleration of change: at y = 0, x = onset wavelength. In the first trial, the instrument…

Once the model was created the formula was used. Finally, a formula was created that could remove the risk from investments. Many financial derivatives were invented to exploit the BS formula. So after the academics received the Nobel price, LTCM (long term capital management) was created (smart guys going to the market). In 1995 the hedge fund LTCM (long term capital management) was created. The…