Analogy making and the structure of implied volatility skew

An analogy based option pricing model is put forward. If option prices are determined in accordance with the analogy model, and the Black Scholes model is used to back-out implied volatility, then the implied volatility skew arises, which flattens as time to expiry increases. The analogy based stochastic volatility and the analogy based jump diffusion models are also put forward. The analogy based stochastic volatility model generates the skew even when there is no correlation between the stock price and volatility processes, whereas, the analogy based jump diffusion model does not require asymmetric jumps for generating the skew

Strong Domination Critical and Stability in Graphs

ABSTRACT In general strong domination number s (G) can be made to decrease or increase by removal of vertices from G. In this paper our main objective is the study of this phenomenon. Further the stability of the strong domination number of a graph G is investigated. Mathematics subject classification : 05C7

Independent monopoly size in graphs

In a graph G = (V, E), a set D subset of V (G) is said to be a monopoly set of G if every vertex v is an element of V-D has at least d (v)/2 neighbors in D. The monopoly size of G, denoted mo(G), is the minimum cardinality of a monopoly set among all monopoly sets in G. The set D subset of V (G) is an independent monopoly set in G if it is both a monopoly set and an independent set in G. The number of vertices in a minimum independent monopoly set in a graph G is the independent monopoly size of G and is denoted by imo(G). In this paper, we study the existence of independent monopoly set in graphs, bounds for imo(G), and some exact values for some standard graphs are obtained. Finally we characterize all graphs of order n with imo(G) = 1; n-1 and n

Minimal, vertex minimal and commonality minimal CN-dominating graphs

We define minimal CN-dominating graph $mathbf {MCN}(G)$, commonality minimal CN-dominating graph $mathbf {CMCN}(G)$ and vertex minimal CN-dominating graph $mathbf {M_{v}CN}(G)$, characterizations are given for graph $G$ for which the newly defined graphs are connected. Further serval new results are developed relating to these graphs

Resolving connected domination in graphs

For an ordered subset W = w1,w2, · · · ,wk of vertices and a vertex v in a connected graph G = (V,E), the (metric) representation of v with respect to W is the k-vector r(v|W) = (d(v,w1), d(v,w2), · · · , d(v,wk)). The set W is a resolving set for G if distinct vertices of G have distinct representations with respect to W. A resolving set of minimum cardinality is called a minimum resolving set and the cardinality of it is a dimension of G, denoted by dim(G). In this paper, we introduce resolving connected domination number rc(G) of graphs. We investigate the relationship between resolving connected domination number, connected domination number, resolving domination number and dimension of a graph G. Bounds for rc(G) are determined. Exact values of rc(G) for some standard graphs are foun

The monopoly in the join of graphs

In a graph G=(V,E), a set M⊆V(G) is said to be a monopoly set of G if every vertex v∈V−M has, at least, d(v)2 neighbors in M. The monopoly size mo(G) of G is the minimum cardinality of a monopoly set among all monopoly sets of G. A join graph is the complete union of two arbitrary graphs. In this paper, we investigate the monopoly set in the join of graphs. As consequences the monopoly size of the join of graphs is obtained. Upper and lower bound of the monopoly size of join graphs are obtained. The exact values of monopoly size for the join of some standard graphs with others are obtained