Here it is another approximation:
Compensatory Narcissistic personality (not in DSM-Axis II)
Variant of Self-Confident Style
Phallic Narcissistic personality
Masochistic/Self -defeating personality
Contrary to popular opinion, serial killers are rarely insane or motivated by hallucinations and/or voices in their heads. Many claim to be, usually as a way of trying to get acquitted by reason of insanity. There are, however, a few genuine cases of serial killers who were compelled by such delusions.
Herbert Mullin slaughtered 13 people after voices told him that murder was necessary to prevent California from suffering an earthquake. (Mullin went to great pains to point out that California did indeed avoid an earthquake during his murder spree.)
Ed Gein claimed that by eating the corpses of women who looked like his deceased mother, he could preserve his mother's soul inside his body. He killed two women who bore passing resemblances to his mother, eating one and being apprehended while in the process of preparing the second woman's body for consumption. He also used the flesh of exhumed corpses to fashion a "woman suit" for himself so that he could "become" his mother, and carried on conversations with himself in a falsetto voice. After his arrest he was placed in a mental facility for the remainder of his life.
So-called missionary killers believe that their acts are justified on the basis that they are getting rid of a certain type of person (often prostitutes or members of a certain ethnic group), and thus doing society a favor. Gary Ridgway and Aileen Wuornos are often described as missionary killers. In Wuornos' case, the victims were not prostitutes, but their patrons. Missionary killers differ from other types of serial killer in that their motive is generally non-sexual. Arguably, Jack the Ripper also fits this role.
This type kills for the sheer pleasure of it, although what aspect they enjoy varies. Yang Xinhai's post capture statement is typical of such killers' attitudes: "When I killed people I had a desire [to kill more]. This inspired me to kill more. I don't care whether they deserve to live or not. It is none of my concern". Some killers may enjoy the actual "chase" of hunting down a victim more than anything, while others may be primarily motivated by the act of torturing and abusing the victim while they are alive. Yet others, like Jeffrey Dahmer, may kill the victim quickly, almost as if it were a chore, and then indulge in necrophilia or cannibalism with the body. Usually there is a strong sexual aspect to the crimes, even if it may not be immediately obvious, but some killers obtain a surge of excitement that is not necessarily sexual, such as Berkowitz, who got a thrill out of shooting young couples in cars at random and then running away without ever physically touching the victims.
-- Gain motivated
Most criminals who commit multiple murders for material ends (such as mob hit men) are not classed as serial killers, because they are motivated by economic gain rather than psychopathological compulsion. There is a fine line separating such killers, however. For example, Marcel Petiot, who operated in Nazi-occupied France, could be classified as a serial killer. He posed as a member of the French Resistance and lured wealthy Jewish people to his home, claiming he could smuggle them out of the country. Instead he murdered them and stole their belongings, killing 63 people before he was finally caught. Although Petiot's primary motivation was materialistic, few would deny that a man willing to slaughter so many people simply to acquire a few dozen suitcases of clothes and jewelry was a compulsive killer and psychopath. However, it is impossible to understand the true motivation in such cases.
This is the most common serial killer. Their main objective for killing is to gain and exert power over their victim. Such killers are sometimes abused as children, which means they feel incredibly powerless and inadequate, and often they indulge in rituals that are linked, often very specifically, to forms of abuse they suffered themselves. One killer, for example, forced young girls to perform oral sex on him, after which he would spank the girl before finally strangling her. After capture, the killer claimed that when he was a child his older sister would force him to perform oral sex on her, then she would spank him in order to terrify him into not telling their parents. The ritual he performed with his victims would negate the humiliation he felt from his abuse as a child, although such relief would only be temporary, and like other such killers, he would soon feel compelled to repeat his actions until eventual capture. (The vast majority of child abuse victims do not become serial killers, of course, meaning that such abuse is not regarded as the sole trigger of such crimes in these cases.) Many power/control-motivated killers sexually abuse their victims, but they differ from hedonistic killers in that rape is not motivated by lust but as simply another form of dominating the victim.
Some serial killers may seem to have characteristics of more than one type. For example, British killer Peter Sutcliffe appeared to be both a visionary and a mission-oriented killer in that he claimed voices told him to clean up the streets of prostitutes.
Alternatively, another school of thought classifies motive as being one of three types: need, greed, or power.